Implicit Differentiation Until this point all the functions we have found the derivative of have been in EXPLICIT form, that is y=___________, we will now find the derivative of functions that are in IMPLICIT form, y and x will be on the same side of the equation and we will need to take the derivative of both Example 2x 2 + y 3 = 4 Guidelines for Implicit Differentiation 1. Differentiate both sides of the equation with respect to x 2. 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 3. Factor dy/dx out of the left side of the quaiton 4. Solve for dy/dx by dividing both sides of the equation by the left hand factor that does not contain dy/dx Example y 3 + y 2 − 5y − x 2 = −4 x 4 + x 2 y 2 = y 2 Determine the slope of the tangent line to the graph of x 2 + 4y 2 = 4 at the point −1
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