Cabiolab

2021-10-08

Derivatives involving other trigonometric functions Find the derivative of the following functions.
$y=\mathrm{tan}x+\mathrm{cot}x$

irwchh

Step 1
Given
$y=\mathrm{tan}\left(x\right)+\mathrm{cot}\left(x\right)$
By using
$\frac{d}{dx}\left[f\left(x\right)+g\left(x\right)\right]=\frac{d}{dx}\left(f\left(x\right)\right)+\frac{d}{dx}\left(g\left(x\right)\right)$
$\frac{d}{dx}\left[\mathrm{tan}\left(x\right)\right]={\mathrm{sec}}^{2}\left(x\right)$
$\frac{d}{dx}\left[\mathrm{cot}\left(x\right)\right]=-{\mathrm{csc}}^{2}\left(x\right)$
Step 2
Differentiate $y=\mathrm{tan}\left(x\right)+\mathrm{cot}\left(x\right)$ with respect to x
$\frac{dy}{dx}=\frac{d}{dx}\left[\mathrm{tan}\left(x\right)+\mathrm{cot}\left(x\right)\right]$
$=\frac{d}{dx}\left[\mathrm{tan}\left(x\right)\right]+\frac{d}{dx}\left[\mathrm{cot}\left(x\right)\right]$
$={\mathrm{sec}}^{2}\left(x\right)-{\mathrm{csc}}^{2}\left(x\right)$

Jeffrey Jordon

Answer is given below (on video)

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