Question

Find f'(0) for the function. Provide an exact answer (meaning no rounding is involved).

Answer 1

The derivative of a function like this is computed with the following formula:

$(e^{f(x)})' = e^{f(x)}\cdot f'(x)$

So, in your case, we have

$f'(x) = e^{x^2+17x} \cdot (2x+17)$

When you evaluate this at 0, you have

$f'(0) = e^0 \cdot 17 = 1\cdot 17=17$