Solveeit Logo
Login

Question

Mathematics Question on Differentiability

If y2=100tan⁡−1x+45sec−1x,y^{2}=100 \tan^{-1}x+45 sec^{-1}x , then dydx=\frac{dy}{dx}=

A

x2−1x2+1\frac{x^{2}-1}{x^{2}+1}

B

x2+1x2−1\frac{x^{2}+1}{x^{2}-1}

C

1

D

00

Answer

00

Explanation

Solution

y2=100tan⁡−1x+45sec⁡−1xy^{2}= 100 \tan ^{-1} x+45 \sec ^{-1} x
+100cot⁡−1x+45cosec⁡−1x+100 \cot ^{-1} x+45 \operatorname{cosec}^{-1} x
=100tan⁡−1x+100cot⁡−1x= 100 \tan ^{-1} x+100 \cot ^{-1} x
+45sec⁡−1x+45cosec⁡−1x+45 \sec ^{-1} x+45 \operatorname{cosec}^{-1} x
=100(tan⁡−1x+cot⁡−1x)= 100\left(\tan ^{-1} x+\cot ^{-1} x\right)
+45(sec⁡−1x+cosec⁡−1x)+45\left(\sec ^{-1} x+\operatorname{cosec}^{-1} x\right)
=100×π2+45×π2= 100 \times \frac{\pi}{2}+45 \times \frac{\pi}{2}
On differentiating both sides w.r.t. XX, we get
2yy′=02 y y^{\prime}=0
⇒y′=0[∵2≠0,y≠0]\Rightarrow y^{\prime}=0 [\because 2 \neq 0, y \neq 0]