Question

Find the derivative of the function.. y = cot2(sin θ).

Answer 1

Answer:

$\displaystyle y' = -2 \cos \theta \cot (\sin \theta) \csc^2 (\sin \theta)$

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \cot^2 (\sin \theta)$

Step 2: Differentiate

1. Basic Power Rule [Derivative Rule - Chain Rule]:                                       $\displaystyle y' = 2 \cot (\sin \theta) \Big( \cot (\sin \theta) \Big)'$
2. Trigonometric Differentiation [Derivative Rule - Chain Rule]:                   $\displaystyle y' = -2 \cot (\sin \theta) \csc^2 (\sin \theta) (\sin \theta)'$
3. Trigonometric Differentiation:                                                                       $\displaystyle y' = -2 \cos \theta \cot (\sin \theta) \csc^2 (\sin \theta)$

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

Unit: Differentiation