# Find the derivative of {eq}y(x) = \dfrac{\sqrt x}{ 2 + x} {/eq}

## Question:

Find the derivative of {eq}y(x) = \dfrac{\sqrt x}{ 2 + x} {/eq}

## Derivative:

If the given function is of the form {eq}y=\frac{f\left( x \right)}{g\left( x \right)}{/eq} that is, the function is in the form of type of fraction and we have to find {eq}\frac{dy}{dx}{/eq} then we can't directly differentiate numerator and denominator separately thus to find {eq}\frac{dy}{dx}{/eq} we will use division rule of differentiation and division rule of differentiation is given as {eq}\frac{dy}{dx}=\frac{g\left( x \right)\frac{d}{dx}\left( f\left( x \right) \right)-f\left( x \right)\frac{d}{dx}\left( g\left( x \right) \right)}{{{\left( g\left( x \right) \right)}^{2}}}{/eq} .

## Answer and Explanation: 1

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Given:

• The given function is {eq}y\left( x \right)=\frac{\sqrt{x}}{2+x}{/eq}.

To find {eq}\frac{dy}{dx}{/eq}.

Differentiating {eq}y\left( x...

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