If f(x)=6arcsin(x^3) find f'(x)

Answer 1

Use the rule for the deriviative of a function of a function.
Let u(v) = 6 arcsinv and v(x)= x^3

f(x) = u(v(x))
f'(x) = du/dv * dv/dx
= [6/sqrt(1-v^2)]* 2x^2
= 12 x^2/sqrt(1-x^6)]

Answer 2

18 x^2/sqrt(1-x^6)

Answer 3

You're right; I typed the wrong coefficient for dv/dx