If$f(x) = g(x) \cdot h(x)$, then$f’(x) = g’(x) \cdot h(x) + g(x) \cdot h’(x)$.

Partial Differentiation

$$𝑢=𝑓(𝑥,𝑦)*𝑔(𝑥,𝑦)$$ $$𝑢_𝑥=\frac{∂𝑢}{∂𝑥}=𝑔(𝑥,𝑦)\frac{∂𝑓}{∂𝑥}+𝑓(𝑥,𝑦)\frac{∂𝑔}{∂𝑥} $$ And,  $$𝑢_𝑦=\frac{∂𝑢}{∂𝑦}=𝑔(𝑥,𝑦)\frac{∂𝑓}{∂𝑦}+𝑓(𝑥,𝑦)\frac{∂𝑔}{∂𝑦}$$