Differentiate the following functions with respect to x:

Question

Differentiate the following functions with respect to x: sin –1 (2x 2 – 1), 0 < x < 1

Philoid · Accepted Answer

Now

Using 2cos²θ – 1 = cos2θ

y = sin^–1(cos2θ)

Considering the limits,

0 < x < 1

0 < cos θ < 1

0 < 2θ < π

0 > –2θ > –π

Now,

Differentiating w.r.t x, we get