Implicit Differentiation of Circle Equation

Calculus 1 · Axiom Academy

EXAMPLE Implicit Differentiation of the Circle Equation Differentiate x^2 + y^2 = 25 implicitly to find the slope at any point on the circle. The circle x^2 + y^2 = 25 is not a function — no single rule gives y from x . Instead of solving for y first, differentiate both sides as they stand , treating y as an unknown function of x . Find , then evaluate the slope of the tangent line at the point (3, 4) .

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