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College+ · Multivariable Calculus

Partial derivatives

140 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    Let f(x,y)=−3x2y+3xy2f(x,y) = -3x^{2}y + 3xy^{2}. Find ∂f∂x\dfrac{\partial f}{\partial x} at the point (x,y)=(4,−2)(x,y) = (4, -2).

  2. Warm-up

    Let f(x,y)=−x2y+3xy2f(x,y) = -x^{2}y + 3xy^{2}. Find ∂f∂x\dfrac{\partial f}{\partial x} at the point (x,y)=(3,−3)(x,y) = (3, -3).

  3. Warm-up

    Let f(x,y)=3x2y−6xy2f(x,y) = 3x^{2}y - 6xy^{2}. Find ∂f∂x\dfrac{\partial f}{\partial x} at the point (x,y)=(3,0)(x,y) = (3, 0).

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