3.6 Implicit Differentiation

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Presentation transcript:

3.6 Implicit Differentiation Niagara Falls, NY & Canada Photo by Vickie Kelly, 2003 Greg Kelly, Hanford High School, Richland, Washington

This is not a function, but it would still be nice to be able to find the slope. Do the same thing to both sides. Note use of chain rule.

This can’t be solved for y. This technique is called implicit differentiation. 1 Differentiate both sides w.r.t. x. 2 Solve for .

Find the equations of the lines tangent and normal to the curve at . We need the slope. Since we can’t solve for y, we use implicit differentiation to solve for . Note product rule.

Find the equations of the lines tangent and normal to the curve at .

Higher Order Derivatives Find if . Substitute back into the equation.

Now let’s do one on the TI-89: Find . APPS Select and press . Calculus Tools ENTER If you see this screen, press , change the mode settings as necessary, and press again. ENTER APPS

Now let’s do one on the TI-89: Find . APPS Select and press . Calculus Tools ENTER Press (Deriv) F2 Press (Implicit Difn) 4 Enter the equation. (You may have to unlock the alpha mode.) Set the order to 2. Press . ENTER

Press and then to return your calculator to normal. ESC HOME p