Question

How do you find the derivative of `y = arcsin ((3x)/4)`?

Answer 1

it's the inverse of the derivative of the inverse function

Explanation:

`4/3 sin y = x`
Now differentiate using `cos y = sqrt (1-sin^2 y)`

`4/3 sqrt(1-9x^2/16) = dx/dy`

or `dy/dx = 3/4(1-9/16 x^2)^(-1/2)`