Question

Derivative of sin (x^(1/3)) + (sinx)^(1/3)

Answer 1

`\bf sin\left( x^{(1)/(3)} \right)+[sin(x)]^{(1)/(3)}\\\\ -------------------------------\\\\ cos\left( x^{(1)/(3)} \right)\cdot \cfrac{1}{3}x^{-(2)/(3)}+\cfrac{1}{3}[sin(x)]^{-(2)/(3)}\cdot cos(x)\impliedby \textit{chain-ruling both terms} \\\\\\ \cfrac{cos(\sqrt[3]{x})}{3\sqrt[3]{x^2}}+\cfrac{cos(x)}{3\sqrt[3]{sin^2(x)}}`

Answer 2

1/3 x^(-2/3) cos (x^1/3) + 1/3(sinx)^-2/3 .cos x