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3.7 Implicit Differentiation. Niagara Falls, NY & Canada. Photo by Vickie Kelly, 2003. Greg Kelly, Hanford High School, Richland, Washington. F4. F3. 2. On the sending unit, press , and then . . 2nd. VAR-LINK. 2nd.

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slide1

3.7 Implicit Differentiation

Niagara Falls, NY & Canada

Photo by Vickie Kelly, 2003

Greg Kelly, Hanford High School, Richland, Washington

slide2

F4

F3

2. On the sending unit, press , and then .

2nd

VAR-LINK

2nd

F7

Press to select .

Calculus Tools

3. On the receiving unit, press .

2nd

VAR-LINK

4. On both units, press (Link).

4. On the receiving unit, select (Receive).

2

5. On the sending unit, select (Send).

1

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.

slide3

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.

slide4

1 Differentiate both sides w.r.t. x.

2 Solve for .

This can’t be solved for y.

This technique is called implicit differentiation.

slide5

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.

slide7

Find if .

Substitute

back into the equation.

Higher Order Derivatives

slide8

Find .

APPS

ENTER

ENTER

APPS

Select and press .

Calculus Tools

If you see this screen, press

, change the mode settings as necessary, and press

again.

Now let’s do one on the TI-89:

slide9

F2

APPS

ENTER

ENTER

Press (Implicit Difn)

4

Press .

Now let’s 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.

slide10

Press and then

to return your calculator to normal.

ESC

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