Question

How do you find the derivative of `f(x)=5e^x`?

Answer 1

`f'(x)=5e^x`

Explanation:

All that is here is a constant, `5`, multiplied with the function `e^x`. When differentiating a function that is multiplied a constant, just differentiate the other function and then multiply that by the constant.

Since the derivative of `e^x` is also `e^x`, when you differentiate the function, the `e^x` remains, and it is also multiplied by the `5`, giving the derivative of, again, `5e^x`.

We can see this as:

`f'(x)=d/dx(5e^x)`

Taking the constant out:

`f'(x)=5*d/dx(e^x)`

Since the derivative of `e^x` is `e^x`:

`f'(x)=5*e^x=5e^x`