Mathematics - Calculus - Multivariable - Partial derivatives - Partial Derivatives

8 steps: (1) For f(x,y), the partial derivative ∂f/∂x treats y as a CONSTANT and differentiates with respect to x only. (2) Example: f(x,y)=x²y+3xy². ∂f/∂x = 2xy+3y² (y is constant). (3) ∂f/∂y = x²+6xy (x is constant). (4) Notation: fₓ, f_x, ∂f/∂x all mean the same thing. (5) Geometric meaning: ∂f/∂