# Differentiating gives wrong result

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Richárd Tóth on 12 Aug 2019
Answered: Alex Mcaulley on 12 Aug 2019
Hello
One of my functions returns this symbolic expression
(10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1
If I use the diff function(by x1) on it, it gives wrong result(ignores the variables or I don't know):
(20000*cos((9*pi)/40)*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40)))/9801 + (20000*sin((9*pi)/40)*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40)))/9801
(50706024009129175657667733171308125*x1)/24848487065673752728138376231780352
If I simply run this code, it works, so something is probably wrong with my returned expression from the function
syms x1 x2
f=(10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
diff(f,x1)

Alex Mcaulley on 12 Aug 2019
Can you show the complete code that generates the symbolic expression? As you say, it works just executing your code.
Richárd Tóth on 12 Aug 2019
Yes, it's not the same code, that code is much longer but gives the same result.
The function:
function expr = testfunc()
syms x1 x2 d1 d2 d3 center1 center2
expr = (cos(d3)*(center1 - x1) - sin(d3)*(center2 - x2))^2/d1^2 + (cos(d3)*(center2 - x2) + sin(d3)*(center1 - x1))^2/d2^2 - 1;
and the code:
syms x1 x2 lambda d1 d2 d3 center1 center2
d1=0.9900;d2=0.9900;d3=9*pi/40;
center1=0;center2=0;
ell = testfunc;
ell = subs(ell);
g = ell;
diff(g,x1)
Running this displays the wrong value I mentioned in previous post.
If you try this, it works:
syms x1 x2
f = (10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
diff(f,x1)

Alex Mcaulley on 12 Aug 2019
I don't know why the result is presented in different way depending on the case, but the result is allways the same:
%Case 1
syms x1 x2
f = (10000*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40))^2)/9801 + (10000*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40))^2)/9801 - 1;
sol = diff(f,x1)
sol =
(50706024009129175657667733171308125*x1)/24848487065673752728138376231780352
double(subs(sol,x1,1))
ans =
2.0406
%Case 2
syms x1 x2 lambda d1 d2 d3 center1 center2
d1=0.9900;d2=0.9900;d3=9*pi/40;
center1=0;center2=0;
ell = testfunc;
ell = subs(ell);
g = ell;
sol = diff(g,x1)
sol =
(20000*cos((9*pi)/40)*(x1*cos((9*pi)/40) - x2*sin((9*pi)/40)))/9801 + (20000*sin((9*pi)/40)*(x2*cos((9*pi)/40) + x1*sin((9*pi)/40)))/9801
sol = simplify(sol)
sol =
(20000*x1)/9801
double(subs(sol,x1,1))
ans =
2.0406