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Implicit differentiation differentiates equations not written as y = f(x), such as x² + y² = 25, by differentiating every term with respect to x and applying the chain rule to y terms. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive eClassroom course walks through each step with worked examples and instant-feedback questions, so you can practise until it's secure.
How you do it
Differentiate both sides with respect to x, treating y as a function of x. Every time you differentiate a y term, multiply by dy/dx by the chain rule. Terms with both x and y need the product rule. Then collect the dy/dx terms and factorise.
Before you start
You will want the chain and product rules at your fingertips first. You meet it in Pure 4. Later work on tangents to curves not written as y = f(x) assumes it.
What you learn
Forgetting it is the single most common mistake in implicit differentiation. The course works through gradients and tangents and putting it together. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
We teach Implicit Differentiation as one of the Differentiation topics in our A-level course library, at the second year of A-level. It runs to 5 concepts, each followed by a check, with 5 worked examples along the way. Nearby topics in the same strand are Increasing & Decreasing Functions, Parametric Differentiation, Product Rule, Quotient Rule and Reciprocal Trig. You can drill this strand further on the Differentiation revision engine, with your accuracy saved to your skill tree.
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