Compute the derivative of the given function below

Question

y=₀∫^{sin^(-1)(x)} cos(t)dt

Answer 1

Let u = sin^–1 x

dy/dx = (dy/du)(du/dx)

(Fundamental Theorem of Calculus)

Plugging in u = sin^–1 x

and recognizing that cos(sin^–1 x) = we get

Alternatively you could simplly solve the integral to show y = x, which means that dy/dx = 1