Cabiolab

2021-05-07

Second-order derivatives Find y" for the following functions

$y=\mathrm{tan}x$

grbavit

Skilled2021-05-08Added 109 answers

Step 1

Here we have to find Second-order derivatives y=?

we have ,$y=\mathrm{tan}x$

Step 2

$y=\mathrm{tan}x$

differentaite with rspect to x

$\frac{dy}{dx}=\frac{d}{dx}\left(\mathrm{tan}x\right)$

$\frac{dy}{dx}={\mathrm{sec}}^{2}x$

differentiate with respect to x

$\frac{{d}^{2}y}{{dx}^{2}}=\frac{d}{dx}{\mathrm{sec}}^{2}x$

$\frac{{d}^{2}y}{{dx}^{2}}=2\mathrm{sec}x\frac{d}{dx}\mathrm{sec}x$

$\frac{{d}^{2}y}{{dx}^{2}}=2\mathrm{sec}x(\mathrm{sec}x\times \mathrm{tan}x)$

$\frac{{d}^{2}y}{{dx}^{2}}=2{\mathrm{sec}}^{2}x\mathrm{tan}x$

$\Rightarrow y=2{\mathrm{sec}}^{2}x\mathrm{tan}x$

Here we have to find Second-order derivatives y=?

we have ,

Step 2

differentaite with rspect to x

differentiate with respect to x

Jeffrey Jordon

Expert2021-11-24Added 2575 answers

Answer is given below (on video)