Q:

Find the derivative of 4/square root of x

Accepted Solution

A:
Answer:[tex]\displaystyle \frac{dy}{dx} = \frac{-2}{x^\Big{\frac{3}{2}}}[/tex]General Formulas and Concepts:CalculusDifferentiationDerivativesDerivative NotationDerivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]Basic Power Rule:f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:Step 1: DefineIdentify[tex]\displaystyle y = \frac{4}{\sqrt{x}}[/tex]Step 2: DifferentiateDerivative Property [Multiplied Constant]:                                                   [tex]\displaystyle y' = 4 \frac{d}{dx} \bigg[ \frac{1}{\sqrt{x}} \bigg][/tex]Basic Power Rule:                                                                                         [tex]\displaystyle y' = 4 \Bigg( \frac{1}{x^\Big{\frac{3}{2}}} \Bigg)[/tex]Simplify:                                                                                                         [tex]\displaystyle y' = \frac{4}{x^\Big{\frac{3}{2}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Differentiation