Question

How do you find the derivative of the function: `y=(sin^-1x)`, at x=3/5?

Answer 1

Derivative of `y=sin^(-1)x` at `x=3/5` is `4/5`

Explanation:

As `y=sin^(-1)x`, we have

`x=siny` and `(dx)/(dy)=cosy`

and `(dy)/(dx)=1/cosy=1/sqrt(1-sin^2y)=1/sqrt(1-x^2)`

and derivative of function at `x=3/5` is

`y'(3/5)=1/sqrt(1-(3/5)^2)=1/sqrt(1-9/25)=1/sqrt(16/25)=1/(4/5)=5/4`
graph{arcsinx [-5, 5, -2.5, 2.5]}