Question

If `y= sec (tan^(-1)x)," then "(dy)/(dx)" at " x = 1` is equal to
A. `1/sqrt2`
B. `1/2`
C. 1
D. `sqrt2`

Answer 1

Correct Answer - A
Given,` y = sec (tan^(1) x) `
Let `" " tan^(-1) x = theta`
` rArr" " x = tan theta`
` :." " y = tan theta = sqrt(1+x^(2)) `
On differentiating w.r.t. X, we get
`(dy)/(dx) = 1/(2sqrt(1+x^(2)) * 2x `
At ` x = 1, " " (dy)/(dx) = 1/(sqrt2) `