Question

What is the derivative of `e^(pi)+pi^(x)`?

Answer 1

`pi^x lnpi`

Explanation:

`e^pi` is a constant

(it's near `2.7^3` using `e~~2.7` and `pi~~3`)

Because it is a constant its derivative is `0`.

(You could use the power rule for `d/dx(u^pi)` to get `pie^(pi-1)*d/dx(e)`, but since `d/dx(e) = 0`, you still end up with `0`. Similarly with treating this as an exponential function you need to multiply by the derivative of the exponent, which is `d/dx(pi) = 0`)

`pi^x` is an exponential function with base `pi`, so its derivative uses the rule:

`d/dx(b^x) = b^x lnb`

So:

`d/dx(pi^x) = pi^x lnpi`