Question

How do you differentiate `y=sin^-1(2x)`?

Answer 1

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

Explanation:

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

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx[sin^-1(f(x))]=1/(sqrt(1-(f(x))^2)).f'(x))color(white)(2/2)|)))`

`y=sin^-1(2x)`

`rArrdy/dx=1/(sqrt(1-(2x)^2)).d/dx(2x)`

`color(white)(rArrdy/dx)=2/(sqrt(1-4x^2))`