Question
The derivative of cos−1(x−1−xx−1+x) at x=−1 is
Answer: Option D
:
D
We have, y=cos−1(x−1−xx−1+x)⇒y=cos−1(1−x21+x2)
Now, Put x=tanθ
We get y=cos−1(1−tan2θ1+tan2θ)⇒y=cos−1(cos2θ)⇒y=2θ⇒y=2tan−1x∴dydx=21+x2∴dydx|x=−1=21+(−1)2=2
Was this answer helpful ?
:
D
We have, y=cos−1(x−1−xx−1+x)⇒y=cos−1(1−x21+x2)
Now, Put x=tanθ
We get y=cos−1(1−tan2θ1+tan2θ)⇒y=cos−1(cos2θ)⇒y=2θ⇒y=2tan−1x∴dydx=21+x2∴dydx|x=−1=21+(−1)2=2
Was this answer helpful ?
More Questions on This Topic :
Question 3.
If y=ln(xa+bx)x,then x3d2ydx2 is equal to
....
Question 5.
If xy=ex−y then dydx=
....
Question 6.
If x=ey+ey+ey+ey+⋯∞
....
Question 7.
If xy.yx=16,then dydx at (2,2) is
....
Submit Solution