Question

What is the derivative of `e^xln2`?

Answer 1

`e^xln2`

Explanation:

First, note that

`d/dx(e^x)=e^x`

Next, recall that `ln2` is a constant, just like `2` or `-5`. This means it gets "carried along" with the differentiation and won't be modified. Thus,

`d/dx(e^xln2)=ln2d/dx(e^x)=e^xln2`

Answer 2

If there is a typo in the question and the intended question was for `e^(xln2)`

Explanation:

In this case, we are differentiating a function of the form `e^u`.

We'll use `d/dx(e^u) = e^u (du)/dx`.

Because `u=xln2` we need the same observation mason m made in the answer to the question as typed, that
`ln2` is simply some constant, so `(du)/dx = d/dx(xln2) = ln2`

We get

`d/dx(e^(xln2) )= e^(xln2)ln2`.