Checking implicit differentiation using Ti83 graphing calculator.

[Baron]

I'm not sure if this is in the right section as there doesn't seem to be a calculator section.

I found an answer to my question from http://qcpages.qc.cuny.edu/~groskes/CalcTI83Derivatives.html, but I don't understand the bolded and underlined part.

5. I have an equation in the form f(X,Z) = 0. I used implicit differentiation to get a formula for dZ/dX. (The formula for dZ/dX is an expression in Z and X.) How can I check my formula for dZ/dX using a TI83 calculator?

Answer: There are many answers to this question. Here is one possible answer:
Put your formula for f(X,Z) into the Y₃ function variable (as an expression in X and Z). Put your formula for the derivative dZ/dX into the Y₂ function variable (also as an expression in X and Z). In Y₁, enter the expression ( -nDeriv(Y₃,X,X) / nDeriv(Y₃,Z,Z) )/ Y₂. (nDeriv can be found in the [MATH] menu. Y[/FONT][/COLOR][SUB]3[/SUB][COLOR=#000000][FONT=Times New Roman] is found in the [VARS] menu.) Remember, the leading minus sign is a small minus. Next, go to the home screen and put a random number into the Z variable. Next, go to [TBLSET] and select "Indpnt:Ask". Finally, press [TABLE] and enter random values for X. (Your values for (X,Z) should be in the domain of f(X,Z).)[/FONT][/COLOR] [COLOR=#000000][FONT=Times New Roman]In your table, all the numbers in the column for Y[/FONT][/COLOR][SUB]1[/SUB][COLOR=#000000][FONT=Times New Roman] should, in general, be equal to the number 1 to about 5 or 6 significant figures. If they are not, then your formula for dZ/dX is probably not correct. (This is because your numerical "implicit derivative" using f(X,Z) (and computed in the function variable Y[/FONT][/COLOR][SUB]1[/SUB][COLOR=#000000][FONT=Times New Roman]) is not giving the same numbers as your function values using the expression for dZ/dX (which is computed in the function variable Y[/FONT][/COLOR][SUB]2[/SUB][COLOR=#000000][FONT=Times New Roman]).) [/FONT][/COLOR][/Quote] When I try adding a formula into the Y[SUB]3[/SUB] function variable, it takes me to the home screen and when I enter the expression using 'test =' I get error. What am I doing wrong? Is there another way to check my answer using a graphing calculator because my teacher always makes us simplify tricky implicit differentiation? Any help will be greatly appreciated.[/MATH]

 

[galactus]

To store a function in a Y variable from the home screen you must enclose it in " ".

The quotes are found by pressing [ALPHA] [+].

Type your expression in quotes. Then, press [STO]. Go to [VARS] and select Y3.

Press ENTER and the calculator will display DONE.

The manual can be found on line if you do not have one.

Here is a screen shot of what you would type. Of course, enter in whatever expression you need.

This is just an example.