Question

derivative of sin cubic root of x multiplied by the cubic root of sin x

Answer 1

\[\frac d{dx} (\sin (\sqrt[3]x)\left(\sqrt[3]{\sin(x)}\right)\]
correct?

Answer 2

correct

Answer 3

interesting... use product rule

\[\large \left(\sin(\sqrt[3]x)\right)\frac{d}{dx} \left(\sqrt[3]{\sin(x)}\right) + \left(\sqrt[3]{\sin(x)}\right) \frac d{dx} \left(\sin (\sqrt[3]x)\right)\]

Answer 4

how would you find the derivatives of cubic root sin x and sin cubic root x?