Question

How do you find derivative of `f(x) = 3 arcsin (x^4)`?

Answer 1

`f'(x)=(12x^3)/sqrt{1-x^8}`

Explanation:

Use the facts that `d/dx(c * f(x))=c * f'(x)` for any constant `c`, `d/dx(arcsin(x))=1/sqrt{1-x^2}` and the Chain Rule `d/dx(f(g(x)))=f'(g(x)) * g'(x)`:

`f'(x)=3*1/sqrt{1-(x^4)^2} * 4x^3=(12x^3)/sqrt{1-x^8}`