Question

How do you find the derivative of `f(x)=3((arcsinx)^2)`?

Answer 1

`f'(x)=(6arcsinx)/(sqrt(1-x^2))`

Explanation:

`•color(white)(x)d/dx(arcsinx)=1/(sqrt(1-x^2))`

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

`"Given "f(x)=g(h(x))" then"`

`f'(x)=g'(h(x))xxh'(x)`

`rArrf'(x)=3[2arcsinx xxd/dx(arcsinx)]`

`color(white)(rArrf'(x))=3(2arcsinx xx1/(sqrt(1-x^2)))`

`color(white)(rArrf'(x))=(6arcsinx)/(sqrt(1-x^2))`