What is the derivative?
f(x) = 5 ^ [(x^2)-(2x)+8]
is this correct>
f ' (x) = 5 ^ {[(x^2)-(2x)] * ln(5) * 2x-2 } * 5^8
?
$\displaystyle \frac{d}{dx}5^{x^2-2x+8}=5^{x^2-2x+8}ln(5)(2x-2)$
The derivative of a constant raised to a function = the same constant raised to the same function times the natural log of the base times the derivative of the function which is in the exponent.
Edit: I think your answer is okay too, I don't see any reason you couldn't split that up into $\displaystyle 5^{x^2-2x}(5^8)$ which would give you the answer that you got. To simplify your answer, you would just end up adding the $\displaystyle 5^8$ back into the $\displaystyle 5^{x^2-2x}$ which would be the same as what is up top.