Question

Find the derivative of 4/square root of x

Answer 1

Answer:

$\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}$

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

$\displaystyle y = \frac{4}{\sqrt{x}}$

Step 2: Differentiate

1. Derivative Property [Multiplied Constant]:                                                   $\displaystyle y' = 4 \frac{d}{dx} \bigg[ \frac{1}{\sqrt{x}} \bigg]$
2. Basic Power Rule:                                                                                         $\displaystyle y' = 4 \Bigg( \frac{1}{x^\Big{\frac{3}{2}}} \Bigg)$
3. Simplify:                                                                                                         $\displaystyle y' = \frac{4}{x^\Big{\frac{3}{2}}}$

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

Unit: Differentiation