Q. 95.0( 1 Vote )

# Differentiate <sp

Answer :

Let and .

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

We have By substituting x = tan θ, we have   [ sec2θ – tan2θ = 1]  u = sin–1(2sinθcosθ)

But, sin2θ = 2sinθcosθ

u = sin–1(sin2θ)

Given 0 < x < 1 x ϵ (0, 1)

However, x = tan θ

tan θ ϵ (0, 1)  Hence, u = sin–1(sin2θ) = 2θ

u = 2tan–1x

On differentiating u with respect to x, we get  We know   Now, we have By substituting x = tan θ, we have   [ sec2θ – tan2θ = 1]  v = cos–1(cos2θ – sin2θ)

But, cos2θ = cos2θ – sin2θ

v = cos–1(cos2θ)

However, Hence, v = cos–1(cos2θ) = 2θ

v = 2tan–1x

On differentiating v with respect to x, we get  We know   We have    Thus, Rate this question :

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