EasyPartial derivativesmultivariable-matrix-calculus-001
Chapter 08 practice bank
100 questions:
Many-Variable Calculus
Solve on paper first. Reveal only the final answer when you want to check yourself. There are no worked solutions in this bank by design.
34 easy 33 medium 33 advanced
EasyPartial derivativesmultivariable-matrix-calculus-002
For f(x,y)=2x²y+y³, find ∂f/∂y.
EasyGradientsmultivariable-matrix-calculus-003
Find ∇(x²+y²) at (3,-3).
EasyDirectional derivativesmultivariable-matrix-calculus-004
For f(x,y)=x²+xy, find the directional derivative at (5,4) along e₁=[1,0].
EasyJacobiansmultivariable-matrix-calculus-005
Find the Jacobian of F(x,y)=[5x+y,x+6y].
EasyHessiansmultivariable-matrix-calculus-006
Find the Hessian of f(x,y)=1x²+3y².
EasyTangent planesmultivariable-matrix-calculus-007
Give the tangent plane to z=xy at (3,3).
EasyJacobian shapesmultivariable-matrix-calculus-008
What is the Jacobian shape for F:ℝ^2→ℝ^3 using outputs as rows?
EasyMatrix calculusmultivariable-matrix-calculus-009
For f(x)=[1,5]x, where x∈ℝ², find ∇ₓf.
EasyDouble integralsmultivariable-matrix-calculus-010