Answer :

Let and v = sin–1(3x – 4x3)

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

We have

By substituting x = tan θ, we have


However, x = tan θ

As tan 0 = 0 and tan = 1, we have .

Thus, lies in the range of tan–1x.


On differentiating u with respect to x, we get

We know and derivative of a constant is 0.

Now, we have v = sin–1(3x – 4x3)

By substituting x = sin θ, we have

v = sin–1(3sinθ – 4sin3θ)

But, sin3θ = 3sinθ – 4sin3θ

v = sin–1(sin3θ)


However, x = sin θ

Hence, v = sin–1(sin3θ) = 3θ

v = 3sin–1x

On differentiating v with respect to x, we get

We know

We have


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