How do I find the Derivative of a Function where the x is a number?

If I was to find d/dx g(1) for example, would I first find the value of the function g(x) at x=1 and then find the derivative of that which becomes 0 because the result would probably be a constant. Or do I first find the derivative of g(x) and then plug in x=1 to calculate it?

Thanks

Answers

Answer 1

Given a function g(x), its derivative, if it exists, is equal to the limit

[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]

The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).

Alternatively, you can directly find the derivative at a point by computing the limit

[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]

But this is essentially the same as the first method, we're just replacing x with 1.

Yet another way is to compute the limit

[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]

but this is really the same limit with h = x - 1.

You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.


Related Questions

How many L of a 10% alcohol solution must be mixed with 9l of a 80% alcohol solution to make a 55% solution

Answers

Answer:

Step-by-step explanation:

The best thing to do for these solution/mixture problems is to make a table:

                          #L           *           %alcohol         =            L alcohol

    10% sol.

+   80% sol.                                                                                            

    55% sol.  

In this way, we can keep track of our information AND figure out the equation we need to use to solve it. Notice first, the equation along the top of the table:

#L * %alcohol = L alcohol  This tells us that we are multiplying the #L column times the %alcohol column to get the L alcohol column. Notice second, that there is a + sign to the far left, indicating that we are ADDING rows 1 and 2 together to get the mix. Let's start filling this in. The easy part is the % alcohol column. 10% alcohol has .10 alcohol as a decimal, likewise for the 80% and 55%:

                          #L             *            %alcohol          =         L alcohol

   10% sol.                                             .10

+  80% sol.                                            .80               =                          

   55% sol.                                            .55

Now to fill in the first column. We know that our unknown, from the problem, is the number of Liters, #L in the 10% solution, so that is x, and we also know that we have 9 L of the 80% alcohol. Filling that in:

                             #L            *             %alcohol           =         L alcohol

  10% sol.                x            *                .10

+ 80% sol.               9           *                 .80                                                

  55%                                                      .55

Now look back at the + sign. We are told that we are mixing the 10% with the 80%, so we are adding them together. So let's do that. We will also follow the rule for the table and multiply the first column times the second column to fill in the last column to complete the table:

                          #L           *             %alcohol            =              L alcohol

   10% sol.           x            *                 .10                  =                 .10x

+  80% sol.          9           *                 .80                  =                  7.2          

  55% sol.      (9 + x)         *                 .55                  =         .55x + 4.95

If we add the 2 solutions together to get the new solution in the first column, we will also add the L alcohol in the last column to get our equation:

.10x + 7.2 = .55x + 4.95 and

- .45x = - 2.25 so

x = 5L

We need 5 Liters of the 10% solution if we want to mix that with 9L of 80% solution to get 14 L of 55% solution.

Connor wants to represent 25 divided by the difference of 12 and seven he writes the expression of ( 25÷12) -7 is Connor expression correct explain

Answers

Step-by-step explanation:

Step 1:  Check to see if Connor is right

25 divided by the difference of 12 and seven

25 / (12 - 7)

Since we have a 12 and seven, that means that we have them together.  However, how Connor is presenting it, it would be 25 divided by 12 subtracted 7.  Therefore, Connor is incorrect.

Answer:

No he's not correct.

Step-by-step explanation: Let's take a step back and look at the question, he wants to represent the difference of 12 and 7 ÷ by 25. Therefore in order to do that we need to figure out the difference 12 and 7 so the equation would look like this 12-7=5  after doing that we divide 5 by 25 so it would look like this 25÷5=5.

So the correct equation is (12-5) ÷25

Hope this helps!

 

The number 55 is attached to a two-digit number on its left, and the formed 4-digit number is divisible by 24. What could be the two-digit number? List all options.

Answers

Answer:

the answer will be 44 I think I hoped I helped if not sorry.

Step-by-step explanation:

Plz someone do this for me I’ll give a lot of points

Answers

Answer:

RW is congruent to WX

Step-by-step explanation:

We know that PW and WV and Angle W is vertical angle so We need to include that RW congruent to WX.

find the least square number which is exactly divisible by 8,12,15&20​

Answers

Answer:

first we need to find the LCM of the given numbers i.e. 8, 12, 15 and 20

2*2*2*5*3=120

Then

as 2, 3, 5 are not in pairs, we need to multiply the LCM with 2*5*3=30

so,

least perfect square number which is divisible by each of numbers 8 12 15 and 20

=120*30=3600

Step-by-step explanation:

Hello can we be friends.....

Karma was given some birthday money. She puts money in an account. Every month after that, she deposits the same amount of money. The equation that models this situation is y=75x+60, where y is the amount of money in the account and x is the number of deposits. What does the y-intercept mean in this situation

Answers

Answer:

y represents the amount in the bank account after 7 months.

Step-by-step explanation:

Let karma gets x money on his birthday.

He has 60 in his account initially

He deposits teh same money for the seven months

So, the money he has after the seven months is 7 x + 60  

According to the question,

y =7 x + 60

It shows that the amount after seven months is y.  

In a fruit cocktail, for every 15 ml of orange juice you need 5 ml of apple juice and 50 ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form?

Answers

Answer:

1:10:3

Step-by-step explanation:

5. Find the measures of the following. Round to the nearest whole number. (2 points)
a. "HT
H
b. 2T
15 cm
c.
ΖΗ
W
8 cm
T

Answers

Solution:-1

[tex] \\ \sf \longmapsto \: HT=√15^2+8^2[/tex]

[tex] \\ \sf \longmapsto \: HT=√225+64[/tex]

[tex] \\ \sf \longmapsto \: HT=√289[/tex]

[tex] \\ \sf \longmapsto \: HT=17cm[/tex]

Solution:-2

Angle T=15x

Let others be 8x and 17x

[tex] \\ \sf \longmapsto \: 8x+17x+15x=180[/tex]

[tex] \\ \sf \longmapsto \: 40x=180[/tex]

[tex] \\ \sf \longmapsto \: x=\dfrac{180}{40}[/tex]

[tex] \\ \sf \longmapsto \: x=4.5[/tex]

[tex] \\ \sf \longmapsto \: 15x=15(4.5)[/tex]

[tex] \\ \sf \longmapsto \: \angle T=67.5°[/tex]

Solution:-3

[tex] \\ \sf \longmapsto \: \angle H=8x[/tex]

[tex] \\ \sf \longmapsto \: \angle H=32.5°[/tex]

En un triángulo ABC, se traza la mediana BM, si AM = 5x - 4 y MC = 3x + 6. Calcula AC.
A) 5 B) 7 C) 14 D) 21 E) 42

Answers

Answer:

A) 5

Step-by-step explanation:

Explain this to me I don't understand

Answers

Answer:

26.124

Step-by-step explanation:

SOH CAH TOA

tan 43 = about 0.933

than times it by 28 and get

26.124

7. La somme de deux multiples de 3 consécutifs est de 129. Quels sont ces deux nombres?

Answers

Answer:

Les deux nombres doivent avoir une différence de 3. Algébriquement, ce serait x + (x + 3) = 129. 2x est alors égal à 126. X est égal à 63 et x + 3 est à 66. Ces nombres sont des multiples consécutifs de 3 dont la somme est de 129.

Step-by-step explanation:

The two numbers must have a difference of 3. Algebraically, it would be x + (x + 3) = 129. 2x then is equal to 126. X equals 63 and x + 3 is 66. These numbers are consecutive multiples of 3 whose sum is 129.

What type of line is PQ?

A. side bisector
B. altitude
C. median
D. angle bisector

Answers

Answer:

D

Step-by-step explanation:

Since ∠ RPQ = ∠ SPQ = 60° , then

PQ bisects ∠ RPS and is an angle bisector

PQ exists the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.

What is angle bisector?

Angle bisector in geometry directs to a line that divides an angle into two equivalent angles. A bisector represents the thing that bisects a shape or an object into two equivalent regions. If we draw a ray that bisects an angle into two equivalent parts of the exact measurement, then it exists named an angle bisector.

It is given that ray PQ is the angle bisector of angle RPS. It means PQ divides the angle RPS in two equivalent parts.

[tex]$m \angle R P Q=m \angle QP S=60^{\circ}$[/tex]

Now, [tex]&m \angle R P S=m \angle R P Q+m \angle Q P S \\[/tex]

[tex]&m \angle R P S=60^{\circ}+60^{\circ} \\[/tex]

[tex]&m \angle R P S=120^{\circ}[/tex]

Therefore, the measure of angle RPS is [tex]$60^{\circ}$[/tex].

Therefore, the correct answer is option D. angle bisector.

To learn more about angle bisector

https://brainly.com/question/24677341

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A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.



Which equation can be used to determine the amount of cherry juice in each mixture?

5q + 3(8 – q) = 36
5q + 3(8 – q) = 8
q + (8 – q) = 8
q + 5 = 5q

Answers

Answer:

I think 5q+3(8-q) =36 is the answer for this question

Based on the amount the restaurant manager spends on the juice mixture, the amount of cherry juice can be found as 5q + 3(8 – q) = 8.

What is the amount of cherry juice used?

Assuming the cherry juice is q and the lime juice is r, the following formulas would be true:

q + r = 8

5q + 3r = 36

The first equation can be rewritten as:

q + r = 8

r = 8 - q

Using substitution into the second formula we get:

5q + 3r = 36

5q + 3(8 - q) = 36

Find out more on simultaneous equations at https://brainly.com/question/16863577.

#SPJ9

Which number belongs to the solution set of the equation?
x + 3 = 45
A. 15
B. 48
C. 43
D. 42

Answers

Answer:

D

Step-by-step explana

[tex] \sf \: The \: value \: of \: x \: is \: the \: number \: that \: belongs \: to \: the \: solution \: \\ \sf \: set \: of \: the \: equation. \: So \: we \: need \: to \: find \: x.[/tex]

[tex] \sf \: x + 3 = 45 \\ \sf \: x = 45 - 3 \\ \sf \: x = \underline{42}[/tex]

Answer ⟶ [tex]\boxed{\bf{D.42}}[/tex]

Which shows a difference of squares?10 y squared minus 4 x squared16 y squared minus x squared8 x squared minus 40 x 2564 x squared minus 48 x 9

Answers

Answer:

16 y squared minus x squared

Step-by-step explanation:

The other all expressions except 16y²-x² doesn't complete the square and its difference. Then we can check 16y²-x²,

Now take the expression 16y²-x² and we can try to solve it.

We can simplify the terms separately to associate them as perfect squares,

→ 16y² = (4y)² --- (1)

→ x² = (1x)² --- (2)

Now we can take the difference of eq. (1) and eq. (2),

→ 16y²-x²

→ (4y)²-(1x)² --- (3)

Now eq. (3) shows a difference of squares.

Another representation is,

→ (4y - x) (4y + x)

→ 16y²- x²

→ (4y)²- (1x)²

Therefore, the expression 16y²-x² shows a correct difference of squares.

Answer:

its b trust

Step-by-step explanation:

Complete the sentence. The amount of time it takes to drive from your house to the library is most likely to be a function of the _____.

Answers

Answer:

D. distance

Step-by-step explanation:

really ? given the choices you needed help with that ?

only D makes sense. the rest is completely ridiculous and has nothing to do with driving from the house to the library.

Evaluate the following expression using the values given: (1 point)

Find 3x − y − 3z if x = −2, y = 1, and z = −2.

Answers

3(-2) - 1 - 3(-2) = -1

A box contains 6 red, 3 white, 2 green, and 1 black (in total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?

Answers

Answer:

Pick at least 4 balls to be sure that you are getting balls with the same color.

Step-by-step explanation:

Here, you want to know the least number of balls to be taken out of the box to be sure that you have all the three colors represented.

You know there are 12 identical balls, with the least numbers of balls being 1 and 2. Hence, to be able to know you have all the colors of balls represented, you will need to have taken all the less represented ones i.e the 1 and 2 , and this means that the next number of ball which would be taken will confidently confirm that you have taken all the colors since you would have exhausted picking other balls at this point.

So you shall be needing at least 4 balls picked to ensure that you have all the colors represented

Does the graph have even symmetry, odd symmetry, or neither ?

Answers

Answer:

Odd symetry I think

Step-by-step explanation:

Sorry I'm new can you be my friend too please?

Hope this helps!:)

Have a nice day.

Keep scrolling for more....

Have a great day

You can do anything you put your mind to

^_^

:)

This is it

what's is 11 divided by 620​

Answers

Answer:

0.017741

Step-by-step explanation:

Determine whether ABC are functions:

A. (2,5) (3,7) (-1,4) (0, 6)
B.(-3, 1) (4, 2) (5,-2) (-3,-1)
C. (3,4) (-4, 6) (-1,0) (0,1)
A.
B.
C.

Answers

Answer:

A. Function

B. Not a function

C. function

Anyone? Ive tried and its not clicking

Answers

Answer:

Hello Bro How Are You....?

here you go. is this correct?

22. If y = 1/3(x - 2), express x in terms of y A. X = 3y - 2 B. x = 3y + 2 C. x=y D. x=-Y​

Answers

Answer:

B. x= 3y+2

Step-by-step explanation:

y=⅓x-⅔

⅔+y=⅓x

(⅔÷⅓)+(y÷⅓)=⅓x÷⅓

2+3y=x

Angle ADB and CD are straight lines.

angle ADC = 5 x angle CDB

Work out the size of angle ADC.

Answers

Answer:

150 degrees

Step-by-step explanation:

5 + 1 = 6

180 : 6 = 30

30 x 5 = 150

Grade improvement and study motivation

Answers

Answer:

yes because we are leraning new things

Which is the graph of f(x) = (x - 1)(x + 4)?
6
4
2
2
22
2
4
6
2
B42
2
O
O
4
2
2

Answers

Answer:

Graph D

Step-by-step explanation:

f(x)=(x-1)(x+4

roots x=1,-4,

x=0, y=-4

OAmalOHopeO

someone please help me

Answers

Step-by-step explanation:

D) (A³/2)³ = A⁹/8

A³ whole to the power 3 is A⁹

2³ is 8

Add 1,249 and 594.
what is their sum rounded to the nearest hundred?

A. 700

B. 1,800

C. 1,900​

Answers

Answer:

1249+592=1843, rounding that you get B, 1,800

This will be C as it is rounded to the nearest 100 as 1,249 plus 594= 1833 we can infer the 1 is from the “thousands” column and the second one is “8” which is the hundreds column now if it’s 5 and above we round up if it’s below 5 we will round down therefore the answer is C-1900

10)
Ka
The longer base of a trapezoid has endpoints of (-2,- 4) and (4,0). The shorter base contains the point (3, 1).
(40)
(2)
We an equation of the line that contains the shorter base of the trapezoid. Provide valid mathematical reasoning and calculations to
you derived your equaiton.
of a trapezoid are parallel
Suation and explanation in the space provided.
Math symbols
Relations
Geometry

Answers

Answer:

y = 2·x/3 - 1

Step-by-step explanation:

The endpoints of the longer base of the trapezoid = (-2, -4), and (4, 0)

The point contained on the shorter base = (3, 1)

The slope of the line representing the longer base, m, is given as follows;

m = (0 - (-4))/(4 - (-2)) = 2/3

The slope of the shorter base = The slope of the longer base = m = 2/3

The equation of the line representing the shorter base in point and slope form is therefore;

y - 1 = (2/3)·(x - 3)

∴ y = 2·x/3 - 2 + 1 = 2·x/3 - 1

The equation of the shorter side of the trapezoid is y = 2·x/3 - 1

What’s 4 divided by $5.32

Answers

Answer:

0.752

Step-by-step explanation:

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