Q. 5 A5.0( 1 Vote )

# Differentiate <sp

Let and.

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

We have

By substituting 2x = cos θ, we have

[ sin2θ + cos2θ = 1]

u = sin–1(2 cos θ sin θ)

u = sin–1(sin2θ)

Given

However, 2x = cos θ

Hence, u = sin–1(sin 2θ) = π – 2θ.

u = π – 2cos–1(2x)

On differentiating u with respect to x, we get

We know and derivative of a constant is 0.

However,

Now, we have

On differentiating v with respect to x, we get

We know

We know and derivative of a constant is 0.

We have

Thus,

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