Q7 of 354 Page 12

Differentiate the following functions with respect to x:
sin^–1 (2x² – 1), 0 < x < 1

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

Differentiate the following functions with respect to x:

sin^–1 (1 – 2x²), 0 < x < 1

Differentiate the following functions with respect to x:

Differentiate the following functions with respect to x:sin–1 (2x2 – 1), 0 < x < 1