Calculus practice

Implicit Differentiation worksheets

Find dy/dx from implicit polynomial equations with separate powers, mixed products and composite powers.

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Find dy/dx for each implicit equation. Treat y as a function of x, and keep product and chain rule factors visible.

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Each worked key keeps the product and chain rule structure visible before solving the grouped equation for the derivative.

Learning objective

Differentiate an implicit relation, collect the terms containing dy/dx, and solve for the derivative.

Worked example

dy/dx = -x/y, where y != 0.

Differentiate both sides to get 2x + 2y(dy/dx) = 0, then isolate dy/dx.

Teaching notes

Treat y as a function of x, so differentiating y introduces dy/dx.
Use the product rule on terms containing both x and y.
State that the denominator in the dy/dx answer must be nonzero on the original curve.

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Choose 8, 10, or 12 problems and any nonempty selection of separate powers, mixed products, and composite powers.

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