Question

What is the derivative of `(3x^3)/e^x`?

Answer 1

`9x^2e^-x -3x^3e^-x = (3x^2 (3-x))/e^x`

Explanation:

Note that `1/e^x = e^-x ->f (x) = 3x^3e^zx`.

Now we can use the product rule. `f (x)=g (x)h (x) -> f'(x) = g'(x)h (x)+f (x)g'(x)`

The power rule and definition of the derivative of `e^u` give us `d/ dx (3x^3) = 9x^2, d/dx (e^-x) = -e^-x`

Thus...

`f'(x) = 9x^2e^-x -3x^3e^-x = (3x^2 (3-x))/e^x`