如何替换mathematica中的函数 [英] How to do substitution of a function in mathematica

问题描述

我有表达式 D[f[x, y], x]，我想用 x* 替换 f[x,y]y，我尝试了以下操作:

I have the expression D[f[x, y], x], and I want to substitute f[x,y] with x*y, I tried the following:

D[f[x, y], x]/.{f[x,y] ->x*y}和D[f[x, y], x]/.{f ->x*y}

但都没有奏效.感谢您的帮助！谢谢.

But neither worked. Would appreciate your help! Thanks.

推荐答案

你的表达式中导数的 FullForm 是

The FullForm of the derivative in your expression is

In[145]:= D[f[x,y],x]//FullForm

Out[145]//FullForm= Derivative[1,0][f][x,y]

这应该可以解释为什么第一条规则失败了 - 您的表达式中不再有 f[x,y] 了.第二条规则失败了，因为 Derivative 认为 f 是一个函数，而你用一个表达式来代替它.你可以做的是:

This should explain why the first rule failed - there is no f[x,y] in your expression any more. The second rule failed because Derivative considers f to be a function, while you substitute it by an expression. What you can do is:

In[146]:= D[f[x,y],x]/.f->(#1*#2&)

Out[146]= y

请注意，围绕纯函数的括号是必不可少的，以避免与优先级相关的错误.

Note that the parentheses around a pure function are essential, to avoid precedence - related bugs.

或者，您可以通过模式定义您的 r.h.s:

Alternatively, you could define your r.h.s through patterns:

In[148]:= 
fn[x_,y_]:=x*y;
D[f[x,y],x]/.f->fn

Out[149]= y

HTH

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