Gorjamskiw

2023-02-19

How to find the derivative of sec x tan x?

Cailyn Knight

Beginner2023-02-20Added 7 answers

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,$=\mathrm{sec}x({\mathrm{tan}}^{2}x+{\mathrm{sec}}^{2}x)$

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,$=\mathrm{sec}x({\mathrm{tan}}^{2}x+{\mathrm{sec}}^{2}x)$

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