Question

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

Answer 1

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

Explanation:

As `y=cos^(-1)(2x+1)`, we have

`cosy=2x+1` and differentiating it using chain rule, we get

`-siny xx (dy)/(dx)=2` or

`(dy)/(dx)=-2/siny=-2/sqrt(1-cos^2y)=-2/sqrt(1-(2x+1)^2)`