Effect of Increment of Variable on Output in a Multivariate Equation
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There is an equation as you can see below. Here, C1, C2 and C3 denote constants, while x and y denote variables.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1453977/image.png)
I want to observe the effect of x on U. In short, will increasing x increase or decrease U? How can I prove this mathematically? I tried using limit but it didn't work because of two different variables. In addition, a constraint such as 40<x<55 can be set for x.
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Star Strider
2023년 8월 9일
편집: Star Strider
2023년 8월 11일
Perhaps taking the partial derivative of U with respect to x (creating a sort of sensitivity function) will do what you want. You can do this symbolically using the diff function:, or numerically using the gradient function.
EDIT — .(11 Aug 2023 at 15:39)
In detail —
syms C_1 C_2 C_3 x y
sympref('AbbreviateOutput',false);
U = (C_1 * y * tan(x+(y/2))) / (C_2 * tan(x+(y/2)) + C_3 * (cos(y)+tan(x)*sin(y) - 1))
dUdx = diff(U,x);
dUdx = simplify(dUdx, 500)
dUdxfcn = matlabFunction(dUdx)
Supply the appropriate variable values and an appropriate vector for ‘x’ to evaluate the function, then plot the evaluated ‘dUdxfcn’ as a function of ‘x’.
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