Gorjamskiw

2023-02-19

How to find the derivative of sec x tan x?

Cailyn Knight

Use the product rule and derivatives of trigonometric functions.
Explanation: $\frac{d}{dx}\left(\mathrm{sec}x\mathrm{tan}x\right)=\frac{d}{dx}\left(\mathrm{sec}x\right)\mathrm{tan}x+\mathrm{sec}x\frac{d}{dx}\left(\mathrm{tan}x\right)$
$=\left(\mathrm{sec}x\mathrm{tan}x\right)\mathrm{tan}x+\mathrm{sec}x\left({\mathrm{sec}}^{2}x\right)$
$={\mathrm{sec}\mathrm{tan}}^{2}x+{\mathrm{sec}}^{3}x$
Thus,$=\mathrm{sec}x\left({\mathrm{tan}}^{2}x+{\mathrm{sec}}^{2}x\right)$

Do you have a similar question?