This question is not enlightening nor is it difficult. But some part of my notation or how I have defined my functions is messing up the D[f,x] function.
In[224]:= Clear[x]
Clear[y]
Clear[a]
Clear[k1]
Clear[k2]
Clear[U]
In[299]:= Attributes[a] = {Constant}
Attributes[k1] = {Constant}
Attributes[k2] = {Constant}
In[275]:= values = {x_ -> 0, y_ -> 0}
In[276]:=
U[x_, y_] :=
k1/2 (Sqrt[(a - x)^2 + (a/Sqrt[3] - y)^2] - (2*a)/Sqrt[3])^2 +
k1/2*(Sqrt[(-a - x)^2 + (-(a/Sqrt[3]) - y)^2] - (2*a)/Sqrt[3])^2 +
k2/2*(Sqrt[(-(a/Sqrt[3]) - x)^2 + (a - y)^2] - (2*a)/Sqrt[3])^2 +
k2/2*(Sqrt[(a/Sqrt[3] - x)^2 + (-a - y)^2] - (2*a)/Sqrt[3])^2
In[199]:= Simplify[U[0, 0], Reals]
Out[199]= 2 ((k1/2)[(2 (-a + Sqrt[a^2]))/Sqrt[3]]^2 + (k2/2)[(
2 (-a + Sqrt[a^2]))/Sqrt[3]]^2)
(**The above output is the correct form that I should be seeing**)
D[U[x, y], x] /. values
Out[258]= 0
In[303]:= D[U[x, y], y] /. values
Out[303]= 0
(**The above are correct outputs according to the problem statement**)
In[304]:= Simplify[D[U[x, y], x, y] /. values, Reals]
Out[304]= 0
(**The above derivative should give:(Sqrt[3]/2k1-Sqrt[3]/2k2) \
according to the problem statement
But for some reason the D[] function is also taking derivates of k1 \
and k2 - which are set as constants
**)
I know this problem has something to do with my notation or the constants k1 and k2. I am new to mathematica, so this may just be a syntax error.
Thanks in advance.
Update: here is the result of my changes, which did output the correct values for my taylor expansion
In[352]:= D[U[x, y], y, x] /. values
Out[352]= (Sqrt[3] k1)/2 - (
3 (-((2 a)/Sqrt[3]) + (2 Sqrt[a^2])/Sqrt[3]) k1)/(4 Sqrt[a^2]) - (
Sqrt[3] k2)/2 + (3 (-((2 a)/Sqrt[3]) + (2 Sqrt[a^2])/Sqrt[3]) k2)/(
4 Sqrt[a^2])
In[354]:= Simplify[D[U[x, y], x, y] /. values, Reals]
Out[354]= (Sqrt[3] a (k1 - k2))/(2 Sqrt[a^2])
Out[303]to be different fromOut[304]? If you wrapSimplifyaround a zero it will still be zero? (You made a comment belowOut[303]saying that this is correct $\endgroup$