# How can I rewrite symbolic expression as a function of another symbolic expression?

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David Jacob on 8 Mar 2021
Answered: Sai Veeramachaneni on 11 Mar 2021
Suppose I want to evaluate an expression of the type with . Let and be functions of x and y, e.g. and . And I am able to show analytically that . Knowing that , I can now rewrite to the expression . With this I can now deduce that if .
However, I want to use a MATLAB script to approximate the exact value of the boundary of the circle/ellipse using a while loop that evaluates at a lower boundary a (where ) and b (where ), so that . However, I do not know how to make MATLAB rewrite my symbolic expression for as a function , so that I can substitute the boundaries a and b. I would be glad about suggestions on how to solve this type of problem.

Sai Veeramachaneni on 11 Mar 2021
Hi,
You can leverage syms, diff functions to implement your functionality
Example:
syms x y
V = x^2+y^2
f1 = x
f2 = -x+y*(2-3*x^2-2*y^2)
g = f1*diff(V,x)+f2*diff(V,y)
Hope it helps