What is the derivative of -cot(2x)?

Answer:

[tex]\displaystyle y' = 2 \csc^2 (2x)[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Basic Power Rule:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Explanation:

Step 1: Define

Identify

[tex]\displaystyle y = - \cot (2x)[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

10. Lindsey is an avid tennis player. She kept track of the number of winners she had per game for an entire season. The shape of the distribution of the number of winners is roughly symmetric and the five- number summary of the number of winners is: Min: 10 Q1: 18 Med: 48 Q3: 79 Max: 92
Luke is Lindsey’s biggest rival. The average number of winners Luke had per game for the season has the same value as Lindsey’s IQR. Who had the greatest average number of winners this season? Explain.
(A)Lindsey, she averaged approximately 48 winners per game while Luke only averaged 18 winners per game.
(B)Lindsey, she averaged approximately 49.4 winners per game while Luke only averaged 48 winners per game.
(C)Luke, he averaged 61 winners per game while Lindsey only averaged approximately 48 winners per game.
(D)Luke, he averaged 61 winners per game while Lindsey only averaged approximately 79 winners per game.
(E)There is not enough information provided to determine Lindsey’s average.​

How do fishing gears cause decrease in the population of marine species?
A) by changing water drifts
B) by decreasing phytoplankton population
by causing loss of habitat
D) by increasing water salinity
Please select the best answer from the choices provided
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