Question 335843
Is that {{{ln(arcsin(x)*x^3)}}}?. This is why it is important to use proper grouping symbols. Perhaps you mean {{{ln(arcsin(x))*x^3}}}?

Anyway, using the former:

If so, we use the chain rule and product rule.

The derivative of the inside times the derivative of the outside.

Derivative of inside using product rule: {{{3x^2*arcsin(x)+x^3/sqrt(1-x^2)}}}

Because the derivative of ln(x)=1/x, the derivative of the outside is: {{{1/(arcsin(x)*x^3)}}}

Multiply them:  {{{(3sqrt(1-x^2)*arcsin(x)+x)/(x*sqrt(1-x^2)*arcsin(x))}}}