Product Rule
If$f(x) = g(x) \cdot h(x)$, then$fβ(x) = gβ(x) \cdot h(x) + g(x) \cdot hβ(x)$.
Partial Differentiation
$$π’=π(π₯,π¦)*π(π₯,π¦)$$ $$π’_π₯=\frac{βπ’}{βπ₯}=π(π₯,π¦)\frac{βπ}{βπ₯}+π(π₯,π¦)\frac{βπ}{βπ₯}Β $$ And,Β $$π’_π¦=\frac{βπ’}{βπ¦}=π(π₯,π¦)\frac{βπ}{βπ¦}+π(π₯,π¦)\frac{βπ}{βπ¦}$$