y = 5.0*10^-10*x +7.0*10^-25*x^3I need to solve equation above for (x) , then differentiate (getting jacobian) for (y)
like:
sol ={solve(y,x)}
diff1= diff(sol,y)
Is that possible?
MATLAB: How to differentiate a non linear equation in Matlab
differential equationsnonlinear
Related Solutions
One approach:
syms x y f(x,y) = exp(x-y) + x^2 + y^2;Dfx = diff(f, x)D2fx = diff(Dfx,x)Dfy = diff(f, y)D2fy = diff(Dfy, y)Inflpt = solve(Dfx, Dfy, [x,y])xs = Inflpt.xys = Inflpt.yCheck = [D2fx(xs,ys); D2fy(xs,ys)]figurefsurf(f, double([xs-2 xs+2 ys-2 ys+2]))Since ‘Check’ is positive for both functions, ‘Inflpt’ is a minimum.
EDIT —
Added plot figure —
You have defined
x = 2:30; y = 40:60;but then you have
syms x yThat is equivalent to
x = sym('x');y = sym('y');which is to say that it overwrites x and y, and afterwards they are no longer numeric. But afterwards you sometimes treat them as symbols and sometimes treat them as numeric. In particular,
[X,Y] = meshgrid(x,y);attempts to treat them as numeric.
You also have
u = @(x,y) 10*sin(200*x)+0.1*cos(10*y)+(100*x)./y; v = @(x,y) 10*cos(200*x)+0.1*sin(10*y)-100*(x./y);ex = diff(u,x);ey = diff(v,y);The two diff() lines attempt to take the symbolic differentiation of a MATLAB function handle. You probably cannot do that. You can differentiate a symbolic expression, and you might be able to differentiate a symbolic function, but probably not a function handle.
ex = diff(u(x,y), x);ey = diff(v(x,y), y)would invoke the function handles on the symbolic parameters x and y, giving a symbolic expression as a result, and that symbolic expression can be differentiated.
Best Answer