Question

What is the derivative of the 5th root of t^3?

Answer 1

$\bf y=t^{\frac{3}{5}}\implies \cfrac{dy}{dt}=\stackrel{\textit{using the power rule}}{\cfrac{3}{5}t^{\frac{3}{5}-1}}\implies \cfrac{dy}{dt}=\cfrac{3}{5}t^{-\frac{2}{5}} \\\\\\ \cfrac{dy}{dt}=\cfrac{3}{5t^{\frac{2}{5}}}\implies \cfrac{dy}{dt}=\cfrac{3}{5\sqrt[5]{t^2}}$