Question

What is the derivative of `e^5`?

Answer 1

The derivative is `0`

Explanation:

Here are three ways to see that the derivative is `0`:

The power rule and chain rule

`d/dx (u^5) = 5u^4 d/dx(u)`

In this case `u = e` is a constant, so we get:

`d/dx (e^5) = 5e^4 d/dx(e) = 5e^4*0 = 0`

Exponential function and chain rule

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

In this case `u = 5` is a constant, so we get:

`d/dx(e^5) = e^5 d/dx(5) = e^5*0 = 0`

`e^5` is a constant

`e ~~ 2.7`, so `e^5` is s a number close to `2.7^5`.

The derivative of that number (a constant) is `0`

`d/dx(e^5) = 0`

Additional note This is a lot like asking for the derivative of `2^5` which is clearly the same as the derivative of `32` which is `0`.

The constant `e` causes confusion until a student gets comfortable with the fact that `e` is just some number.

Asking about the derivative of `x^e` also causes confusion .