Second-order derivatives Find y" for the following functions y=tan⁡x

Step 1 Here we have to find Second-order derivatives y=? we have , y=tan⁡x Step 2 y=tan⁡x differentaite with rspect to x dydx=ddx(tan⁡x) dydx=sec2x differentiate with respect to x d2ydx2=ddxsec2x d2ydx2=2sec⁡xddxsec⁡x d2ydx2=2sec⁡x(sec⁡x×tan⁡x) d2ydx2=2sec2xtan⁡x ⇒y=2sec2xtan⁡x

"Second-order derivatives Find y" for the following functions..." solved and explained

Cabiolab

Answered question

2021-05-07

Second-order derivatives Find y" for the following functions

y = \tan x

Answer & Explanation

grbavit

Skilled2021-05-08Added 109 answers

Step 1
Here we have to find Second-order derivatives y=?
we have ,

y = \tan x

Step 2

y = \tan x

differentaite with rspect to x

\frac{d y}{d x} = \frac{d}{d x} (\tan x)

\frac{d y}{d x} = \sec^{2} x

differentiate with respect to x

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} \sec^{2} x

\frac{d^{2} y}{{d x}^{2}} = 2 \sec x \frac{d}{d x} \sec x

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

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

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

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

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