Question

How do you differentiate `y=arcsin(x^2)`?

Answer 1

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

Explanation:

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

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

`y=arcsin(x^2)`

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

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