Given:
[tex]y=x^{\frac{8}{5}}[/tex]To find:
The first derivative of the function.
Explanation:
Differentiating with respect to x, we get
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(x^{\frac{8}{5}}) \\ =\frac{8}{5}x^{\frac{8}{5}-1} \\ =\frac{8}{5}x^{\frac{8-5}{5}} \\ =\frac{8}{5}x^{\frac{3}{5}} \end{gathered}[/tex]Final answer:
The first derivative of the given function is,
[tex]\frac{dy}{dx}=\frac{8}{5}x^{\frac{3}{5}}[/tex]