Not a fan of Leibniz notation? We can do implicit differentiation with Lagrange notation just as well.
Things to remember for implicit differentiation with Lagrange notation:
- x' = 1.
- since y is a function of x, any derivative involving y must use the chain rule.
- since y is a function of x, taking the derivative of xy (or of any other product involving both x and y) requires the product rule.
- since y is a function of x, taking the derivative of
(or any other quotient involving both x and y) requires the quotient rule.