Question

How do you find the derivative of `sin^-1 * (5x)`?

Answer 1

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

Explanation:

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(sin^-1 x)=1/(sqrt(1-x^2)))color(white)(a/a)|)))`

differentiate using the `color(blue)"chain rule"`

`rArrd/dx(sin^-1(5x))=1/(sqrt(1-(5x)^2)).d/dx(5x)`

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