Question

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

Answer 1

Answer:

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

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

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

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

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

Explanation:

Step 1: Define

Identify

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

Step 2: Differentiate

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

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

Unit: Differentiation