If y = sin^-1 x + cos^-1 x, find dy/dx.

Question

If y = sin^-1 x + cos^-1 x, find \(\cfrac{dy}{d\mathrm x} \).

Answer 1

We know that  sin^-1x+ cos^-1x = \(\cfrac{\pi}2\)

So, here y = sin^–1 x + cos^–1 x

= \(\cfrac{\pi}2\) which is a constant.

Also, sin^-1 x and cos^-1 x exist only when -1 ≤ x ≤ 1

So, \(\cfrac{dy}{d\mathrm x} \) = 0 when x ∈ [-1, 1] and does not exist for all other values of x.