Differentiation in several variables

Concepts

• Function of several variables 10 exercisesA function of several variables f assigns to each point mathbf x=(x_1,dots,x_n) of a set D⊆mathbb R^n, its domain, a single real…
• Limit of a function of several variables 10 exercisesThe limit of a function f at a point mathbf a is the number L that the values f(mathbf x) approach as mathbf x gets close to math…
• Level curve 10 exercisesA level curve of a function f of two variables is the set of points in the plane where f takes one same constant value c.
• Partial derivative 10 exercisesThe partial derivative of a function f(x,y) with respect to x at a point (a,b) is the ordinary derivative of the one-variable fun…
• Tangent plane 10 exercisesThe tangent plane to the graph of a function f(x,y) at the point (a,b,f(a,b)) is the plane that best approximates the surface nea…
• Differentiability in several variables 10 exercisesA function f(x,y) is differentiable at a point (a,b) if its graph has a tangent plane there: the error of the linear approximatio…
• Gradient 10 exercisesThe gradient ∇ f of a differentiable function f is the vector that collects its partial derivatives at a point; it points where f…
• Directional derivative 10 exercisesThe directional derivative D_uf of f at a point x_0, along a unit vector u, is the rate of change of f moving from x_0 in the dir…
• Chain rule in several variables 10 exercisesThe chain rule for z=f(x,y), with x=x(t) and y=y(t), gives the derivative of the composition as the sum of what each intermediate…