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

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

Ответ:

jackkkkk32

17.01.2022

Mathematics

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

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

Basic Power Rule:

f(x) = cxⁿf’(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

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

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

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