Ok, I am going through the MIT Open Course ware course on single variable calculus. I have never taken calculus before, so I apologize of this is a really trivial question.
I know that with $f(x)=x^n$ then f'(x)=nx^{n-1}.
Without using this trick and fully working it out I can't seem to come to the derivative of $f(x)=80-5x^2$.
I basically boil it down to $(-5/dx)(x+dx)(x+dx)$. I cannot seem to get $dx$ out of the denominator so that I don't have a division by zero as $dx$ tends to 0... Am I brain farting something here or is this why I should just skip to the aforementioned shortcut?