Question

What is the derivative of e^x/3

Answer 1

Answer:

$\frac{1}{3}e^{\frac{x}{3}}$

Step-by-step explanation:

The given expression is

$e^{\frac{x}{3} }$

Let

$y=e^{\frac{x}{3} }$

We can rewrite this as

$y=e^{\frac{1}{3}x }$

This is of the form

$y=e^{ax}$

The derivative of exponential functions in this form is given by;

$\frac{dy}{dx}=ae^{ax}$

This implies that;

$\frac{dy}{dx}=\frac{1}{3}e^{\frac{x}{3}}$

Hence the derivative of the given function is

$\frac{1}{3}e^{\frac{x}{3}}$

Answer 2

Answer:

$\frac{1}{3}e^{x/3}$

Step-by-step explanation:

Derivative

$\frac{1}{3}e^{x/3}$

Since, the derivative of e^x is e^x and e^(yx) is ye^(yx)