Calculus 3.7

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3.7 Implicit Differentiation
Niagara Falls, NY Canada
Greg Kelly, Hanford High School, Richland,
Washington
Photo by Vickie Kelly, 2003
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Before we start, we are going to load the
Calculus Tools flash application software to your
calculator.
1. Connect the sending and receiving calculators
together.
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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.
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This cant be solved for y.
This technique is called implicit differentiation.
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Find the equations of the lines tangent and
normal to the curve
at .
Note product rule.
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Find the equations of the lines tangent and
normal to the curve
at .
tangent
normal
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Higher Order Derivatives
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Now lets do one on the TI-89
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Now lets do one on the TI-89
Find .
Select and press
.
Calculus Tools
Press (Deriv)
Enter the equation. (You may have to unlock the
alpha mode.)
Set the order to 2.
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