Question

What is the derivative of e^x/3

Answer 1

`(1)/(3)e^{(x)/(3)}`

Explanation:

The given expression is

`e^{(x)/(3) }`

Let

`y=e^{(x)/(3) }`

We can rewrite this as

`y=e^{(1)/(3)x }`

This is of the form

`y=e^(ax)`

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

`(dy)/(dx)=ae^(ax)`

This implies that;

`(dy)/(dx)=(1)/(3)e^{(x)/(3)}`

Hence the derivative of the given function is

`(1)/(3)e^{(x)/(3)}`

Answer 2

`(1)/(3)e^(x/3)`

Explanation:

Derivative

`(1)/(3)e^(x/3)`

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