# Whole derivation of two variable differential function

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Minjae Cho on 22 Jun 2022
Commented: Walter Roberson on 22 Jun 2022 I am struggleing with the whole derivation of differential equation.
Can y'all give me an advice how to implement that into a code?
I've tried using diff() but diff(f(x,y), y) gives 1 not y'.

James Tursa on 22 Jun 2022
Please show the code you are using.
y' means derivative of y with respect to x, not derivative of y with respect to y. You should be taking derivative of f(x,y) with respect to x, not y.
##### 2 CommentsShowHide 1 older comment
Walter Roberson on 22 Jun 2022
Is there any way to get a whole derivative rather than a partial derivative?
syms x y
f = y - x^3 + x + 1
f = dy = f
dy = df = diff(f, x) + diff(f, y)
df = simplify(subs(df, diff(y,x), dy))
ans = You may notice that this is not what you wanted... but it satisfies at least one plausible definition of what a "whole derivative" means.
I recommend that you re-examine that derivative provided. I think you will find that it makes no sense unless it is the derivative with respect to x with the assumption that y is a function of x

Walter Roberson on 22 Jun 2022
The equations are being careless about which variables depend on which variables, and on which variable the differentiation is with respect to.
syms x y(x)
f = y - x^3 + x + 1
f(x) = dy = f
dy(x) = df = diff(f, x)
df(x) = simplify(subs(df, diff(y,x), dy))
ans(x) = ##### 2 CommentsShowHide 1 older comment
Walter Roberson on 22 Jun 2022
Plug what values into y(x) ?
syms x y(x) yx
f = y - x^3 + x + 1
f(x) = dy = f
dy(x) = df = diff(f, x)
df(x) = sol = simplify(subs(subs(df(x), diff(y,x), dy), y, yx))
sol = [X, Y] = ndgrid(linspace(-1, 1, 15));
solgrid = double(subs(sol, {x, yx}, {X, Y}));
whos
Name Size Bytes Class Attributes X 15x15 1800 double Y 15x15 1800 double cmdout 1x33 66 char df 1x1 8 symfun dy 1x1 8 symfun f 1x1 8 symfun sol 1x1 8 sym solgrid 15x15 1800 double x 1x1 8 sym y 1x1 8 symfun yx 1x1 8 sym
surf(X, Y, solgrid) 