Question

find the derivative of 1/x^4/3

Answer 1

Answer:

$\displaystyle \frac{dy}{dx} = \frac{-4}{3x^5}$

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

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = \frac{\frac{1}{x^4}}{3}$

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:                                                 $\displaystyle y' = \frac{1}{3} \frac{d}{dx} \bigg[ \frac{1}{x^4} \bigg]$
2. Rewrite:                                                                                                         $\displaystyle y' = \frac{1}{3} \frac{d}{dx}[x^{-4}]$
3. Basic Power Rule:                                                                                         $\displaystyle y' = \frac{1}{3}(-4x^{-5})$
4. Simplify:                                                                                                         $\displaystyle y' = \frac{-4}{3x^5}$

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

Unit: Differentiation