Question

If

$y=tan(4\sqrt{x}+5)$ find $dy/dx$

Answer 1

$y=tan(4\sqrt{x}+5)$

To find $\frac{dy}{dx},$ use chain rule

$\Rightarrow \frac{dy}{dx}=\frac{d}{dx}tan(4\sqrt{x}+5)$

$=se{c}^2(4\sqrt{x}+5)\frac{d}{dx}(4\sqrt{x}+5)$

$=se{c}^2(4\sqrt{x}+5).4.\frac{d}{dx}\left(\sqrt{x}\right)$

$=4se{c}^2(4\sqrt{x}+5).\frac{1}{2\sqrt{x}}.\frac{dx}{dx}$

$=\frac{2}{\sqrt{x}}se{c}^2(4\sqrt{x}+5)$