Whole derivation of two variable differential function

2022 6 22
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更新时间：2022 6 22
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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'.

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回答（2 个）

James Tursa
James Tursa 2022-6-22

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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.

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Minjae Cho
Minjae Cho 2022-6-22
编辑：Minjae Cho 2022-6-22
syms x y
f(x, y) = -x^3 + x + 1 +y;
the derivation should be f '(x, y) => y ' - 3*x^2 + 1
but when I do diff(f, x) => - 3*x^2 + 1 [which is partial derivative w.r.t. x].
Is there any way to get a whole derivative rather than a partial derivative?
Walter Roberson
Walter Roberson 2022-6-22
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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

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Walter Roberson
Walter Roberson 2022-6-22
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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) = 

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Minjae Cho
Minjae Cho 2022-6-22
编辑：Minjae Cho 2022-6-22
then how can I plug the value to y(x)?
ex) later on I have to plug value y=3 to y(x)
Walter Roberson
Walter Roberson 2022-6-22
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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)

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