Question

(sin 9x)'
what is the derivative of sin 9x​

Answer 1

`\displaystyle (d)/(dx)[\sin(9x)] = 9 \cos(9x)`

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)`

Explanation:

Step 1: Define

Identify

`\displaystyle y = \sin(9x)`

Step 2: Differentiate

1. Trigonometric Differentiation [Derivative Rule - Chain Rule]:
   `\displaystyle y' = \cos(9x)(9x)'`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = 9 \cos(9x)(x)'`
3. Basic Power Rule:
   `\displaystyle y' = 9 \cos(9x)`

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

Unit: Differentiation