Evaluation of an Error function [duplicate]

Question

How to evaluate df function in the following code sample?

    f[x_,y_]:=Sqrt[x^4-4x^2 y^2]
    df[x_,y_,dx_,dy_]:=Sqrt[(D[f[x,y],x]dx)^2+(D[f[x,y],y] dy)^2]
    df[1,2,0.2,0.3]

General::ivar: 1 is not a valid variable. >> General::ivar: 2 is not a valid variable. >>

:= says to evaluate the right hand side later when the function is called. Next df[1,2,0.2,0.3] sets x equal to 1 and y equal to 2. Next evaluate the right hand side doing D[f[1,2],1] and you don't know how to differentiate with respect to 1. Same for 2. If you change the := to = in your definition of the df function and you clear all definitions or restart Mathematica then the right hand side is evaluated before df[1,2..2,.3] and the error message goes away. But you must be very careful with this to be certain that the answer is correct. — Bill, Commented May 15, 2019 at 3:55
It works for this sample, but it does not twork for more complicated code which contains many functions. — Emad Raslan, Commented May 15, 2019 at 4:21
Please read this tutorial on how to differentiate := and =. It will help you in other contexts too. — Roman, Commented May 15, 2019 at 7:50

Carl Woll · Accepted Answer · 2019-05-15 05:34:42Z

1

Use Derivative instead of D in your definitions:

df[x_,y_,dx_,dy_] = Sqrt[(Derivative[1,0][f][x,y] dx)^2+(Derivative[0,1][f][x,y] dy)^2];

Then:

df[1, 2, .2, .3]

0. + 0.95219 I

answered May 15, 2019 at 5:34

Carl Woll

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$\begingroup$ I suppose that df[x_,y_,dx_,dy_]=Sqrt[(D[f[x,y],x]dx)^2+(D[f[x,y],y] dy)^2] would work $\endgroup$
– Claude Leibovici
Commented May 15, 2019 at 10:01
$\begingroup$ Yes, the same @ClaudeLeibovici $\endgroup$
– Emad Raslan
Commented May 16, 2019 at 8:44
$\begingroup$ many thanks for you @Carl Woll $\endgroup$
– Emad Raslan
Commented May 17, 2019 at 21:33

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