Implicit Differentiation

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Presentation transcript:

Implicit Differentiation

Differentiate both sides of the equation with respect to x. Thm: Implicit Differentiation: Given an equation involving x and y and assuming y is a differentiable function of x, we can find as follows Differentiate both sides of the equation with respect to x. Collect all terms involving on the left side of the equation and move all other terms to the rights side of the equation. Factor out of the left side of the equation. Solve for by dividing both sides of the equation by the left-hand factor that does not contain

Ex 1: find given that

Ex 2: determine the slope of the tangent line and the tangent line to the graph of at the point .

Ex 3: use implicit differentiation to find for

Ex 4: Find dy/dx by implicit differentiation and evaluate the derivative at the indicated point. y = sin (xy) ,(π/2, 1)

Hwk: p 167, #1-41 odd