Question

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

Or, t to the power of 3/5.
(I'm having difficulty finding a place that clearly explains the hows of dealing with fraction exponent derivatives.)

Answer 1

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