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Calculating mixed partial derivatives of a function A(x,y)

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Caleb
Caleb 2016-4-3
评论： Roger Stafford 2016-4-3
I have a script in MATLAB to calculate the value of a function A. I have also programmed the analytic derivatives of A with respect to x and y and also d2A/dxdy. Now, I want to check that my analytic derivatives are correct with a numerical validation. The form of the function is very complicated, so it's not so easy as just re-checking my math. How would you program the numerical derivative of a mixed partial derivative in MATLAB?

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Roger Stafford
Roger Stafford 2016-4-3
编辑：Roger Stafford 2016-4-3
syms x y
f(x,y) = x*sin(y);
d2fdxdy = diff(diff(f,x),y); % = cos(y)
Another way is:
syms x y
diff(x*sin(x*y),x,y); % = 2*x*cos(x*y)-x^2*y*sin(x*y)
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Caleb
Caleb 2016-4-3
Additionally, if my function contains expressions that are functions of x and y, such as: A(x,y) = x*cos(y) + y*C(x,y), how is that handled?
Roger Stafford
Roger Stafford 2016-4-3
@Caleb: Obviously you cannot find derivatives of such a function without having an explicit expression for C(x,y).
C(x,y) = ..... % <-- whatever you define C as in terms of x and y
A(x,y) = x*cos(y) + y*C(x,y);
d2Adxdy = diff(A,x,y);
See:
http://www.mathworks.com/help/symbolic/diff.html

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