Question

What is the derivative of this function `sin^-1 (5x)`?

Answer 1

`(sin^(-1)(5x))'=5/sqrt(1-25x^2)`

Explanation:

Recall:

`(sin^(-1)u)'=1/sqrt(1-u^2)`

By the above rule (`u=5x`) along with Chain Rule,

`(sin^(-1)(5x))'=1/sqrt(1-(5x)^2)cdot(5x)' =5/sqrt(1-25x^2)`

I hope that this was clear.

Answer 2

`5/(sqrt(1-25x^2))`

Explanation:

`color(orange)"Reminder " d/dx(sin^-1x)=1/(sqrt(1-x^2))`

`"and " d/dx(sin^-1(f(x)))=(f'(x))/(sqrt(1-f(x)^2)`

`rArrd/dx(sin^-1(5x))`

`=5/(sqrt(1-(5x)^2))`

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