Answer:
[tex]\frac{1}{3}e^{\frac{x}{3}}[/tex]
Step-by-step explanation:
The given expression is
[tex]e^{\frac{x}{3} }[/tex]
Let
[tex]y=e^{\frac{x}{3} }[/tex]
We can rewrite this as
[tex]y=e^{\frac{1}{3}x }[/tex]
This is of the form
[tex]y=e^{ax}[/tex]
The derivative of exponential functions in this form is given by;
[tex]\frac{dy}{dx}=ae^{ax}[/tex]
This implies that;
[tex]\frac{dy}{dx}=\frac{1}{3}e^{\frac{x}{3}}[/tex]
Hence the derivative of the given function is
[tex]\frac{1}{3}e^{\frac{x}{3}}[/tex]
