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.)
[tex]\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}}[/tex]
