Implicit Differentiation

AP Calculus · Axiom Academy

LESSON Implicit Differentiation Finding derivatives when y is defined implicitly Step 1: What is Implicit Differentiation? Usually, functions are given explicitly: . We can solve for y directly. But sometimes, y is defined implicitly by an equation. For example: This is a circle. y cannot be solved for explicitly as a single function. Implicit differentiation lets us find without solving for y first! The secret is to treat y as a function of x, even though we can't write it explicitly. When you differentiate terms containing y, use the Chain Rule: This is the key! Every time you differentiate a term with y, multiply by . Step 3: Steps for Implicit Differentiation Differentiate both sides of the equation with respect to x Apply the chain rule to every term with y: multiply by Collect all terms with on one side You've mastered implicit differentiation! Next: Higher-order derivatives—finding f'', f''', and beyond.

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