Derive polynomial gradients from first principles
Use the limit definition, rather than quoting the power rule
\[f(z)=2z\]
\[f\prime(-1)=\lim_{h\to0}\frac{f(-1+h)-f(-1)}{h}\]
\[h\ne0\quad\text{while the quotient is simplified}\]
The input is fixed before forming the quotient. This is a valid way to find a derivative at one point
\[z=-1\]