Consider the function F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2. A) differentiate F(x) B)What is the gradient at the point (2,440)

A point of notation:
'#' is the beginning of a comment, we will use comments to note down thoughts and tricks at each stage of the problem
A) let f(x) denote the differential of F(x)
F(x)=17(x^4)+13(x^3)+12(x^2)+7x+2 # start by rewriting out the question so you can see clearly what you have to do
f(x)=(174)(x^3)+(133)(x^2)+(122)(x^1)+7 #differentiate term by term, x^4 first then x^3 and so on...
f(x)=56(x^3)+39(x^2)+24x+7 #finished. sanity check - does this make sense? why?
B) Let A be the point (2,4) #x=2 and y=440
sub in x=2 to f(x) #we have a function of x, and want to know what that function is at x=2
so we have; f(2)= 56*(2^3)+39*(x^2)+24*(2)+7f(2)=448+156+48+7f(2)=659