Question

Differentiate rmula1" title=" \sqrt{x} + \frac{1}{5x} - 3" alt=" \sqrt{x} + \frac{1}{5x} - 3" align="absmiddle" class="latex-formula">
with respect to their variable ​

Answer 1

$\\ \tt\longmapsto \dfrac{d}{dx}\sqrt{x}+\dfrac{1}{5x}-3$

$\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}-3$

• Derivative of any constant is 0

$\\ \tt\longmapsto \dfrac{d}{dx}x^{\frac{1}{2}}+5x^{-1}$

$\boxed{\sf \dfrac{d(x^n)}{dx}=nx^{n-1}}$

$\\ \tt\longmapsto \dfrac{1}{2}x^{\frac{-1}{2}}-5x^{-2}$

$\\ \tt\longmapsto \dfrac{x}{2}^{\frac{-1}{2}}-\dfrac{1}{5x^2}$

$\\ \tt\longmapsto -\sqrt{\dfrac{x}{2}}-\dfrac{1}{5x^2}$