Worked examples

Differential calculus in several variables

One sheet for each type of problem, with several worked examples of increasing difficulty: first the computation, then the explanation in words. Each sheet starts with links to the theory it uses.

• 1Computing partial derivatives and the gradient
• 2Studying differentiability with the definition
• 3Directional derivatives and direction of steepest ascent
• 4Tangent plane to the graph
• 5Chain rule
• 6Second derivatives and Hessian matrix
• 7Second-order Taylor polynomial