Question

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

Answer 1

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

Explanation:

We can use here the formula for derivative of `sin^(-1)x`, which is `d/(dx)sin^(-1)x=1/sqrt(1-x^2)`

As such to find derivative `(dy)/(dx)` for `y=sin^(-1)2x` using chain rule is given by

`(dy)/(dx)=1/sqrt(1-(2x)^2)xxd/(dx)(2x)`

= `2/sqrt(1-4x^2)`