Question

What is the derivative of this function `(1-sin(x))^(-1/2)`?

Answer 1

`cosx/(2(1-sinx)^(3/2))`

Explanation:

`f(x) = (1-sinx)^(-1/2)`

`f'(x) = -1/2(1-sinx)^(-3/2) * d/dx(1-sinx)` (Power rule and Chain rule)

`f'(x) = -1/2(1-sinx)^(-3/2) * (0-cosx)`

`f'(x) = cosx/(2(1-sinx)^(3/2))`