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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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3.7 Implicit Differentiation

Niagara Falls, NY & Canada

Photo by Vickie Kelly, 2003

Greg Kelly, Hanford High School, Richland, Washington


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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.


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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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1 Differentiate both sides w.r.t. able to find the slope.x.

2 Solve for .

This can’t be solved for y.

This technique is called implicit differentiation.


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We need the slope. Since we can’t solve for able to find the slope.y, we use implicit differentiation to solve for .

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

Note product rule.



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Find if . curve at .

Substitute

back into the equation.

Higher Order Derivatives


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Find . curve at .

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:


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F2 curve at .

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.


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Press and then curve at .

to return your calculator to normal.

ESC

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