What is the derivative of square root of 2x?

Accepted Solution

Answer:[tex]\displaystyle \frac{d}{dx}[\sqrt{2x}] = \frac{\sqrt{2}}{2\sqrt{x}}[/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⁻¹Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)[/tex]Step-by-step explanation:Step 1: DefineIdentify[tex]\displaystyle y = \sqrt{2x}[/tex]Step 2: DifferentiateBasic Power Rule [Derivative Rule - Chain Rule]:                                       [tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{2x}} \cdot \frac{d}{dx}[2x][/tex]Basic Power Rule [Derivative Property - Multiplied Constant]:                 [tex]\displaystyle \frac{dy}{dx} = \frac{2}{2\sqrt{2x}}[/tex]Simplify:                                                                                                         [tex]\displaystyle \frac{dy}{dx} = \frac{1}{\sqrt{2x}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)Unit: Differentiation