# Differentiate <sp

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 :

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