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Advanced Placement (AP)

26.08.2020 23:17

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

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

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Diodorant

Diodorant

4,9(14 marks)

$\displaystyle y' = 2 \csc^2 (2x)$

General Formulas and Concepts:

Calculus

Differentiation

DerivativesDerivative Notation

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

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

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

Explanation:

Step 1: Define

Identify

$\displaystyle y = - \cot (2x)$

Step 2: Differentiate

Trigonometric Differentiation [Derivative Rule - Chain Rule]: $\displaystyle y' = - \big(- \csc^2 (2x) \big)(2x)'$ Simplify: $\displaystyle y' = \csc^2 (2x)(2x)'$ Basic Power Rule [Derivative Property - Multiplied Constant]: $\displaystyle y' = 2 \csc^2 (2x)$

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

Unit: Differentiation

cristymarinee9207

cristymarinee9207

4,8(91 marks)

what the hell is this sh.it omg lma.

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