Q. 175.0( 1 Vote )

Differentiate with respect to if

Answer :

Let and.


We need to differentiate u with respect to v that is find.


We have


By substituting x = sin θ, we have




[ sin2θ + cos2θ = 1]



= tan–1(tanθ)


Given


However, x = sin θ




Hence, u = tan–1(tanθ) = θ


u = sin–1x


On differentiating u with respect to x, we get



We know



Now, we have


By substituting x = sin θ, we have




[ sin2θ + cos2θ = 1]


v = sin–1(2sinθcosθ)


v = sin–1(sin2θ)


However,


Hence, v = sin–1(sin 2θ) = 2θ.


v = 2sin–1(x)


On differentiating v with respect to x, we get




We know




We have





Thus,


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.