Whole derivation of two variable differential function

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Minjae Cho 2022-6-22

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评论： Walter Roberson 2022-6-22

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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Answer 1

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 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 2022-6-22

在 MATLAB Online 中打开

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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Answer 2

Walter Roberson 2022-6-22

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https://ww2.mathworks.cn/matlabcentral/answers/1746100-whole-derivation-of-two-variable-differential-function#answer_991440

在 MATLAB Online 中打开

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 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 2022-6-22

在 MATLAB Online 中打开

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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