Home
Class 12
MATHS
What is the derivative of tan^(-1)((sqrt...

What is the derivative of `tan^(-1)((sqrtx-x)/(1+x^(3//2)))` at x = 1?

A

`-(1)/(4)`

B

`(1)/(2)`

C

`(3)/(2)`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
Let `y=tan^(-1)((sqrtx-x)/(1+x^(3//2)))=tan^(-1).(sqrtx-x)/(1+sqrtx.x)`
`=tan^(-1)sqrtx-tan^(-1)x`
On differentiating w.r.t. we get
`(dy)/(dx)=(1)/(1+x).(1)/(2sqrtx)-(1)/(1+x^(2))`
Now, `((dy)/(dx))_(x=1)=(1)/(1+1).(1)/(2)-(1)/(1+1)=(1)/(4)-(1)/(2)=-(1)/(4).`
Promotional Banner

Similar Questions

Explore conceptually related problems

The derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x)) writ.tan^(-1)x is

Prove that the derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x))" w.r.t. "tan^(-1)x is independent of x.

IF y=tan^-1((sqrtx-x)/(1+x)^(3/2)) then y'(1) is

Derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x))w.r.t.tan^(-1)x is

The derivative of tan^(-1) ((2x)/(1-x^(2))) with respect to cos^(-1) sqrt(1 - x^(2)) is

Find the derivative of tan^(-1)(2x)/(1-x^(2))quad w.r.t sin^(-1)(2x)/(1+x^(2))

Find the derivative of 2/(x+1)-x^(2)/(3x-1) .