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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

The topic of this lecture is “Implicit Differentiation”. If you own a TI-89 calculator, it is capable of performing implicit differentiation when it has the “Calculus Tools” software installed. You may want to install this software before you continue this lecture. You have two options to complete this installation: Option 1: Download the free TI Connect TM software to your computer to connect your computer to your calculator. You can use an internet search to find this. Then use the “shop” option to locate the free “Calculus Tools” software, and download it to your calculator. Option 2: If you have a friend who already has the “Calculus Tools” software, you can transfer the program to your calculator using the instructions on the next slide.

Instructions for transferring the Calculus Tools flash application software from another TI-89 to your calculator. 1. Connect the sending and receiving calculators together. 2. On the sending unit, press, and then. 2nd VAR-LINK 2nd F7 Press to select.F4 Calculus Tools 3. On the receiving unit, press. 2nd VAR-LINK 4. On both units, press (Link).F3 5. On the receiving unit, select (Receive).2 6. On the sending unit, select (Send).1

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.

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.

Now let’s do one on the TI-89: 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 Find.

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