Mathematics High School

Use the Product Rule to find the derivative of :
a.[tex]y=(3x-1)^3(2x+5)[/tex]

b. [tex]y=(3x-2)(2x^2+3)[/tex]

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the product rule

Given

y = f(x)g(x) , then

[tex]\frac{dy}{dx}[/tex] = f(x).g'(x) + g(x).f'(x) ← product rule

(a)

let

f(x) = (3x - 1)³ , then using the chain rule

f'(x) = 3(3x - 1)² × [tex]\frac{d}{dx}[/tex](3x - 1) = 3(3x - 1)² × 3 = 9(3x - 1)²

let

g(x) = 2x + 5 ⇒ g'(x) = 2

Then

[tex]\frac{dy}{dx}[/tex] = (3x - 1)³ . 2 + (2x + 5) × 9(3x - 1)²

    = 2(3x - 1)³ +9(3x - 1)²(2x + 5) ← factor out (3x - 1)²

    = (3x - 1)²[ 2(3x - 1) + 9(2x + 5) ]

    = (3x - 1)² [ 6x - 2 + 18x + 45 ]

    = (3x - 1)²(24x + 43)

--------------------------------------------------------------

(b)

let

f(x) = 3x - 2 ⇒ f'(x) = 3

let

g(x) = 2x² + 3 ⇒ g'(x) = 4x

Then

[tex]\frac{dy}{dx}[/tex] = (3x - 2).4x + (2x² + 3). 3 ← distribute parenthesis

    = 12x² - 8x + 6x² + 9

    = 12x² - 8x + 9

Note

It is usual to simplify after differentiating the expressions

Related Questions

PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPP

Felix worked at a music shop during the summer. The table below shows some of Felix’s hours and earnings. The amount of money he earned is proportional to the number of hours he worked.


2. Let x represent the number of hours he worked, y represents the amount of money he earned.Write an equation that represents this relationship.



3. If Felix worked 180 hours, then how much money did he earn?

Answers

Answer:

2. y=9x

3. 180*9 = 1620

Step-by-step explanation:

2. y = mx+b, so find the slop efirst

lacampanella avatar

so take the first two points you got

lacampanella avatar

(2,18) and (5,45),

lacampanella avatar

(45-18)/(5-2) = 9

lacampanella avatar

then use (2,18)

lacampanella avatar

18= 9*2+b

lacampanella avatar

so b=0

3. y = 9x

x= 180. y = 9*180 = 1620

3х - 2y = 1 in standard form

Answers

Answer:

y= (3x-1)/2

Step-by-step explanation:

chicken wings, chicken tenders or chicken nuggets

Answers

Answer:

Chicken wings and tender and nuggets YUMMMMM

Step-by-step explanation:

chicken wings with barbecue sauce


What is the equation of the line
with the points (1, 4) and (5, 12)?
12

Answers

Answer:

y = 2x + 2

Hope you have a great day!

Please help Due Tomorrow

Answers

Answer:

O

Step-by-step explanation:

They reflected the image but when you closely look at it you can see that F is in the same spot as O so they are congruent.

Hope this helps :)


XY zand ABC are similar. If angle X is 32 degrees and angle Y is 84
degrees, find the measure of angle C.

Answers

Answer:

B

Step-by-step explanation:

A triangle always has a degree total of 180. x+y=116 180-116=64 therefore the last angle, angle c, must be 64 degrees.

Answer: B. 64 degrees

Step-by-step explanation:

∠C = 180° - (∠X + ∠Y)

∠C = 180° - (32° + 84°) = 180° - 116° = 64°

Find the exact length of the third side.
35
28

Answers

Answer:

44.821869662

Step-by-step explanation:

How many presents would shelia wrap in 6 hours if she wrapped 4 presents every 4 minutes?

Answers

Answer:96

Step-by-step explanation:

Well 4 presents every 4 minutes is the same thing as 1 present every 1 minute.
So now, we know that every 1 minute, she wraps 1 present.
Now, in 6 hours, there are 360 minutes so, we would simply multiply 1 present by 360 minutes which gives us the answer of 360 presents wrapped in 6 hours.
Glad I could help and also, can you please mark my answer as the brainliest answer?
Thank you so much!

What percent of offspring will be blue eyed?

0%
25%
50%
100%
Please I need help

Answers

Answer:

I believe the answer is 0% because the blue eye trait is recessive.

Step-by-step explanation:

Hope this helps!

✧◝(⁰▿⁰)◜✧

Answer:

25%

Step-by-step explanation:

blue eyes are the resesive gene but there is still a 25% chance.

What is the area of the base?​

Answers

Answer:

40

Step-by-step explanation:

What is 990-990
I need correct answers only

Answers

Answer:

according to my calculations the answer will be 0

Answer:

990 - 990 = 0

Step-by-step explanation:

 990

 990

- ____

  000

Identify the GCF that was factored out of the polynomial -7t2 -42t -49

Answers

Answer:

-7

Step-by-step explanation:

You could take out a factor of -7.

-7t²/-7 = t²

-42t/-7 = 6t

-49/-7 = 7

So the GCF is -7.

I need help with the question please! I'm having a hard time answering it!

Answers

Answer:

small packet: 1.56/22=£0.071

medium: 2.87/38=£0.076

large: 4.67/65=£0.072

small packet is best as it has the lowest price per nail

The expression 17x is equivalent to the expression x 7.

Answers

Answer:

False

Step-by-step explanation:

There is not a one in the 2 expression listed

what is the value of x? -6x=90
Please show you got the answer

Answers

Answer:

-15

Step-by-step explanation:

-6x = 90

x = 90 ÷ -6

x = -15

Answer:

X = -15

Step-by-step explanation:

90/-6 is equal to -15.

You divide the number from the side with the variable from the other side of the = sign.

Rectangle describe in your own words​

Answers

Answer:

A shape with four sides with two being longer than the other two?

Step-by-step explanation:

Answer:

A geometric shape with two sets of paralel lines joined by 4 vertexes.

19/3+___+5/2=10 4/5 I don’t know it

Answers

Answer:

Blank space= 1.96

I'LL GIVE BRAINLIEST TO WHOEVER ANSWERS THE QUESTION CORRECTLY!!!!

A.) 6 units
B.) 10.7 units
C.) 5.5 units
D.) 3 units

Answers

5.5 units??????

please tell me if im right

Answer:

D

Step-by-step explanation:

Expand.
Your answer should be a polynomial in standard form.
(9+ m)(-m +9)=

Answers

Answer: -1m²+81

Step-by-step explanation:

correct standard form means that the terms are ordered from biggest exponent to lowest exponent.The leading coefficient is the coefficient

of the first term in a polynomial in standard form.

FoR example, (9+ m) (-m+9) = *(m+9) (-m+9) *m(-m+9) +9 (-m+9)* -1.mm+9m +9(-m+9) * -1m² +9m +9(-m+9) *-1m²+9m- 9m +81

answer -1m²+81

I NEED HELP PLEASE ANSWER

Answers

Answer:

C

Step-by-step explanation:

Brainliest to right answer

Answers

I think it would be neither, sorry if I’m wrong-

A jar has 2 pennies, 5 nickels, 3 dimes, and 2 quarters. What is the probability of drawing a penny,
replacing it, and drawing another penny?

Answers

There is a 2 in 12 chance of drawing a penny

Step-by-step explanation:

Answer: 2/12

Step-by-step explanation:

There are 12 coins all together, and 2 pennies which means there is a 2/12 chance to draw a penny. Then they replace the penny and draw another time, so by replacing the penny the probability doesn't change and there is still a 2/12 chance of drawing a penny.

WILL MARK BRAINLIEST TO THE BEST ANSWERS. The interior angles of a pentagon measure x°, (2x)°, (2.5x)° , (x + 10)° , and (2x + 20)°. Determine the value of x. PLEASE SHOW ALL SOLUTIONS NESSICARY. THANK YOU.......

Answers

Answer:

x=60

Step-by-step explanation:

The sum of interior angles of a regular Pentagon is 540°

x+2x+2.5x+x+10+2x+20=540

8.5x=540-30

8.5x=510

x=510/8.5=60

Answer:

x = 60°

Step-by-step explanation:

Sum of interior angles of a regular polygon is:

180°(n-2)

Pentagon has 5 sides, so sum of angles is:

180°(5-2) = 180°*3 = 540°

For the given pentagon we have sum of angle measures as below, and solving for x:

x + 2x + 2.5x + (x +10) + (2x + 20) = 540°8.5x + 30° = 540°8.5x = 510°x = 510°/8.5x = 60°

1/2n + 2n + 3/2n - 1

Answers

Answer:

B

Step-by-step explanation:

Answer:

next question is a1= 1 and r=2

have a nice day :)

Step-by-step explanation:

Calvin evaluated Negative two-thirds times 5 and one-sixth using the steps below.

Step 1: Negative two-thirds time (5 + one-sixth)
Step 2: (Negative two-thirds + 5) times (Negative two-thirds + one-sixth)
Step 3: 4 and one-third times negative one-half
Step 4: Negative 2 and one-sixth

Which describes Calvin’s error?
In step 1, he incorrectly broke up 5 and one-sixth.
In step 2, he distributed the Negative two-thirds instead of the 5.

Answers

Answer:

The answer is C on Edge 2021

Step-by-step explanation:

In step 2 he confused the multiplication and addition signs

Answer:

C

Step-by-step explanation:

got it right

HELPPPP

Predict the number of sales in month 5.
The store sold fewer blue jeans
after the
new pants became popular.
Enter the correct answer.
7904
3952
1976
988
?

Answers

494 is the correct answer i got it right on edmentum
494
Explanation: the sales are being cut in half every month
Yw. ;)

(-5,2) and (1,-2) what’s the rise/run?

Answers

Answer:

m= -2/3

Step-by-step explanation:

Use the slope formula to find the slope m .

-3/2 is correctttttttttttttttt

Fellow brains pls help.... Is this true or false?

Answers

Tis true my friend

Y=x anything means True

Ship A sights ship B on a bearing of 308°. What is the bearing of A from B?


I need an explanation on how to do this please. I just learned this but I'm still confused.
Oh, and if you can, please include a picture!
Thank you!

Answers

Answer:

128°

Step-by-step explanation:

the answer is 128° i explained it as i could in the diagram hope you understand

The ratio of children to adults in a supermarket is 1 : 5
There are 15 children in the supermarket.
How many adults are in the supermarket?
pls answer quickly thanks :)

Answers

Answer: There are 75 Adults in the supermarket ask me why if you want a full on explanation. The full on reason of why it is 75 is because if you have a ratio of 1:5 and you now the one is for the kids and it is 15. Then you add 15 from 1 until you get to the 5th ratio. Hence, it brings you all the way to 75 adults. I hope this helped you, and anyone else

Step-by-step explanation:

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