I have the following equation:
$$ \frac{x}{\left[1+C(\eta)(x-1)\right]^3} $$
I want to take the derivative of this function with respect to $\eta$.
How would I do this? Do not worry about what $C(\eta)$ is but clearly the derivative would have to have $C'(\eta)$ in it.
Normally, I would think this is easy, but my numerical solver disagrees with my derivative.
Just treat $x$ as a constant and use the power rule and chain rule to get $-3(x-1)C'(\eta)\dfrac{x}{[1+C(\eta)(x-1)]^4}$.