If$f(x) = \frac{g(x)}{h(x)}$, then$f’(x) = \frac{g’(x) \cdot h(x) - g(x) \cdot h’(x)}{[h(x)]^2}$.

Partial Differentiation

$$𝑢=\frac{𝑓(𝑥,𝑦)}{𝑔(𝑥,𝑦)}, \text{where}\ 𝑔(𝑥,𝑦)≠0$$ $$𝑢_𝑥=\frac{𝑔(𝑥,𝑦)\frac{∂𝑓}{∂𝑥}−𝑓(𝑥,𝑦)\frac{∂𝑔}{∂𝑥}}{[𝑔(𝑥,𝑦)]^2}$$ And $$𝑢_𝑦=\frac{𝑔(𝑥,𝑦)\frac{∂𝑓}{∂𝑦}−𝑓(𝑥,𝑦)\frac{∂𝑔}{∂𝑦}}{[𝑔(𝑥,𝑦)]^2}$$