Question

Differentiate the following functions with respect to x :

$log\left(\frac{1}{\sqrt{x}}\right)+5x^a-3a^x+3\sqrt{x^2}+6^4\sqrt{x^{-3}}$

Answer 1

$\frac{d}{dx}\{log\left(\frac{1}{\sqrt{x}}\right)+5x^a-3a^x+3\sqrt{x^2}+6^4\sqrt{x^{-3}}\}$

$=\frac{d}{dx}log\left(\frac{1}{\sqrt{x}}\right)+5\frac{d}{dx}\left(x^a\right)-3\left(a^x\right)+\frac{d}{dx}+\left(\sqrt[3]{3x^2}\right)+6\frac{d}{dx}\left(\sqrt[4]{4x^{-3}}\right)$

$=\frac{-1}{2}\frac{1}{x}+5a{x}^{a-1}-3a^{x}loga+\frac{2x^{\frac{-1}{3}}}{3}+6x^{\frac{-7}{4}}\left(\frac{-3}{4}\right)$

$=\frac{-1}{2x}+5a{x}^{a-1}-3a^{x}loga+\frac{2x^{\frac{-1}{3}}}{3}-\frac{9}{2}{\times }^{\frac{-7}{4}}$