Question

Whats the derivative of `sin^-1 * (5x)`?

Answer 1

See explanation

Explanation:

Set `arcsinx=cos^(-1)x` hence we know that

`d((arcsinx))/dx=1/(sqrt(1-x^2)`

hence for a function `u(x)`

`d(arcsinu(x))/dx=1/sqrt(1-u^2(x))*du/dx`

hence for `u=5x` we get

`d(arcsin5x)/dx=5/(sqrt(1-25x^2))`