Question

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

Answer 1

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

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (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 (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

Step-by-step 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