Question

How do you find the derivative of the inverse function `f(x)=sin(arccos t)`?

Answer 1

Using trigonometry, rewrite the function.

`f(t)=sin(arccost)` is the sine of an angle in quadrant 1 or 2, whose cosine is `t`.

The sine of such an angle is `sqrt (1-t^2)`.

`f(t) = sqrt (1-t^2)`.

`f'(t)=1/(2sqrt(1-t^2))(-2t) = - t/sqrt (1-t^2)`.