Implicit Differentiation

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Presentation transcript:

Implicit Differentiation Equations hard to solve for y

Function defined Implicitly Definition Differentiating with Respect to x

Implicit Differentiation

Implicit Differentiation

Guidelines for Implicit Differentiation Differentiate both sides of the equation with respect to x. Collect all terms involving dy/dx on the left side of the equation and move all other terms to the right side of the equation. Factor dy/dx out of the left side of the equation. Solve for dy/dx by dividing both sides of the equation by the left-hand factor that does not contain dy/dx.

Implicit Differentiation Representing a Graph by Differentiable Functions Finding the Slope of a Graph Implicitly Determining a Differentiable Function Examples More examples

Finding the Second Derivative Given

Finding a Tangent Line to a Graph Find equations for the tangent line and the normal line to the curve at the given point.

Optical Illusions Section Project p. 140