College · advanced
Multivariable Calculus
Partial derivatives, gradients, and higher-dimensional technique.
Skills
12 skills in 3 sections — fundamentals first, then more specific topics. Practice each until Mastery Score 100.
A.Partial derivatives & gradient8 skills
- A.1 Partial DerivativesPractice →Compute first partials of simple multivariable polynomials.
- A.2 Mixed PartialsPractice →Compute f_xy for simple polynomials.
- A.3 Second Partial DerivativesPractice →Compute f_xx or f_yy of a monomial in x and y.
- A.4 Gradient VectorsPractice →Find ∇f for simple functions of two variables.
- A.5 Gradient MagnitudePractice →Find |∇f| for a linear function of x and y.
- A.6 Directional DerivativesPractice →Compute ∇f · u for f = x² + y².
- A.7 Multivariable Chain RulePractice →Compute dz/dt when z depends on x(t) and y(t).
- A.8 Critical Points of Quadratic SurfacesPractice →Find where both partials vanish for a paraboloid.