Finding the derivative of a quadratic function at a particular point
The question states:
Suppose $f(x)=-5x^2+x-3$.
Find $f'(-1)$.
So I worked out the problem as follows:
\begin{align*} f'(-1)&=\lim_{h\to 0}\frac{-5(h^2+1)+h-13}{h} \\
&=\frac{-5h^2+h-18}{h} \\
&=\frac{h^2\left(-5+\frac{h}{h^2}-\frac{18}{h^2}\right)}{h^2\left(\frac{h}{h^2}\right)}
\end{align*} In which the third step I assume I am doing it wrong because
I believe factoring out only works if I have an expression in the
denominator instead of just the variable $h$.
Would anyone mind telling me where I am going wrong in this problem?
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