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Presentation transcript:

3.7 Implicit Differentiation Niagara Falls, NY & Canada Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2003

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.

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

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

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

Now let’s do one on the TI-89 Titanium: Find. impDiff( The catalog tells you what you need to enter. Equation Variable Dependent Variable Order  (This is the letter i, above the 9.) CATALOG I Note: If your TI-89 Titanium does not have the impDif command, you need to update your software. This command is not available on the old black TI-89 calculator.