Need help evaluating results of implicit differentiation.



#2

Hi everybody,

After I do implicit differentiation on my 50G, and solve for d1y(x), I have my result, which is d1y(x) = expression in terms of
x and y(x). So far so good. Now I want to plug constants in for x and y(x) and evaluate my derivative at a point. This is where I'm having trouble. I can't store a constant in the variable y(x), because that is apparently not a valid variable name. I tried using the define command to create a user function setting y(x) equal to a constant
..IE y(y(x))=3 , but that did not seem to work.
Is there any way to tell the calc that y(x) is equal to 3 when evaluating the results of my implicit differentiation?

Thanks, and best regards, Hal


#3

It seems like the easiest thing to do would be to go into Equation Editor, select Y(X) with the cursor, and replace it with 3.

However, I can imagine situations where that wouldn't work (if there are a lot of Y(X)'s in the result and it would be tedious to replace them all by hand, or if you wanted to automate it with a program).

So here's another way. When you have your expression, enter 'Y(X)' on the stack. Hit DERVX so you have d1Y(X) on the stack (or just enter 'd1Y(X)' to begin with). Then enter some other variable that you're not using, like Z. Then =, SUBST.

Now you can enter 'Y(X)', 3, =, SUBST, and it'll substitute in, leaving the derivative alone (otherwise, it thinks you're saying Y(x) is the constant 3, so its derivative is 0).

You just have to solve for Z now rather than d1Y(X). Or if you really want it back the other way, 'Z=d1Y(X)' SUBST at the end also works.


#4

Actually, if you've already solved for d1Y(X)=f(X,Y(X)), and you just want to evaluate the right side, you could just take the right side of the equation and do the 'Y(X)=3' SUBST step.

(You can take the right side of an equation with OBJ->, DROP, DROP, SWAP, DROP)

I was thinking about a more general situation, in which you either haven't solved for d1Y(X) yet, or for which it might be impossible to solve for it (except numerically)


#5

Thanks very much. The SUBST command was exactly the function I was looking for. It works perfectly.
Best regards, Hal


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