Differentiate the function. y = sqrt x (x-4)


Differentiate the function.

{eq}y = \sqrt x\ (x-4) {/eq}


Derivative of {eq}\displaystyle y {/eq} with respect to {eq}\displaystyle x {/eq} is given by {eq}\displaystyle \frac{dy}{dx} {/eq}.

Product rule of differentiation:

{eq}\displaystyle (uv)'=uv'+vu' {/eq}.

Formula Used:

{eq}\displaystyle (x^n)'=nx^{n-1} {/eq}.

Answer and Explanation:

Given function {eq}\displaystyle y = \sqrt x (x-4) {/eq}.

Differentiating the function with respect to {eq}\displaystyle x {/eq}.

{eq}\displaystyle \begin{align} \frac{dy}{dx}&=\frac{d}{dx}(\sqrt x (x-4))\\ &=\frac{1}{2\sqrt x}(x-4)+\sqrt x\\ &=\frac{\sqrt x}{2}-\frac{2}{\sqrt x}+\sqrt x\\ &=\frac{3}{2}\sqrt x-\frac{2}{\sqrt x}. \end{align} {/eq}

Learn more about this topic:

Calculating Derivatives of Polynomial Equations

from Math 104: Calculus

Chapter 9 / Lesson 4

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