Simplify Derivative with Substitution

up vote
3
down vote

favorite

I try to evaluate:

$$ frac{partial}{partial x} log{u(x, y, z)}$$

Mathematica gives:

$$ frac{1}{x+y+z}$$

I want to simplify the expression with my function:

$$ frac{1}{u(x, y, z)}$$

How to do that?

Thanks.

u[x_, y_, z_] = x + y + z

Simplify[D[Log[u[x, y, z]], x]]

asked 8 hours ago

R zu

1797

New contributor

add a comment |

up vote
3
down vote

favorite

I try to evaluate:

$$ frac{partial}{partial x} log{u(x, y, z)}$$

Mathematica gives:

$$ frac{1}{x+y+z}$$

I want to simplify the expression with my function:

$$ frac{1}{u(x, y, z)}$$

How to do that?

Thanks.

u[x_, y_, z_] = x + y + z

Simplify[D[Log[u[x, y, z]], x]]

asked 8 hours ago

R zu

1797

New contributor

add a comment |

up vote
3
down vote

favorite

I try to evaluate:

$$ frac{partial}{partial x} log{u(x, y, z)}$$

Mathematica gives:

$$ frac{1}{x+y+z}$$

I want to simplify the expression with my function:

$$ frac{1}{u(x, y, z)}$$

How to do that?

Thanks.

u[x_, y_, z_] = x + y + z

Simplify[D[Log[u[x, y, z]], x]]

asked 8 hours ago

R zu

1797

New contributor

I try to evaluate:

$$ frac{partial}{partial x} log{u(x, y, z)}$$

Mathematica gives:

$$ frac{1}{x+y+z}$$

I want to simplify the expression with my function:

$$ frac{1}{u(x, y, z)}$$

How to do that?

Thanks.

u[x_, y_, z_] = x + y + z

Simplify[D[Log[u[x, y, z]], x]]

calculus-and-analysis simplifying-expressions

asked 8 hours ago

R zu

1797

New contributor

asked 8 hours ago

R zu

1797

New contributor

asked 8 hours ago

R zu

1797

New contributor

asked 8 hours ago

R zu

1797

asked 8 hours ago

R zu

1797

New contributor

R zu is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

add a comment |

2 Answers
2

active

oldest

votes

up vote
5
down vote

accepted

D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

add a comment |

up vote
3
down vote

An alternative is to define UpValues instead of DownValues of u:

Derivative[1, 0, 0][u] ^:= 1&

Derivative[0, 1, 0][u] ^:= 1&

Derivative[0, 0, 1][u] ^:= 1&



D[Log[u[x, y, z]], x]

answered 6 hours ago

Carl Woll

65.6k285171

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

add a comment |

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2 Answers
2

active

oldest

votes

2 Answers
2

active

oldest

votes

up vote
5
down vote

accepted

D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

add a comment |

up vote
5
down vote

accepted

D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

add a comment |

up vote
5
down vote

accepted

D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

edited 8 hours ago

answered 8 hours ago

kglr

172k8194399

answered 8 hours ago

kglr

172k8194399

answered 8 hours ago

kglr

172k8194399

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

add a comment |

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

A more general substitution: /. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
8 hours ago

@Rzu, good point.
– kglr
8 hours ago

add a comment |

up vote
3
down vote

An alternative is to define UpValues instead of DownValues of u:

Derivative[1, 0, 0][u] ^:= 1&

Derivative[0, 1, 0][u] ^:= 1&

Derivative[0, 0, 1][u] ^:= 1&



D[Log[u[x, y, z]], x]

answered 6 hours ago

Carl Woll

65.6k285171

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

add a comment |

up vote
3
down vote

An alternative is to define UpValues instead of DownValues of u:

Derivative[1, 0, 0][u] ^:= 1&

Derivative[0, 1, 0][u] ^:= 1&

Derivative[0, 0, 1][u] ^:= 1&



D[Log[u[x, y, z]], x]

answered 6 hours ago

Carl Woll

65.6k285171

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

add a comment |

up vote
3
down vote

An alternative is to define UpValues instead of DownValues of u:

Derivative[1, 0, 0][u] ^:= 1&

Derivative[0, 1, 0][u] ^:= 1&

Derivative[0, 0, 1][u] ^:= 1&



D[Log[u[x, y, z]], x]

answered 6 hours ago

Carl Woll

65.6k285171

An alternative is to define UpValues instead of DownValues of u:

Derivative[1, 0, 0][u] ^:= 1&

Derivative[0, 1, 0][u] ^:= 1&

Derivative[0, 0, 1][u] ^:= 1&



D[Log[u[x, y, z]], x]

answered 6 hours ago

Carl Woll

65.6k285171

answered 6 hours ago

Carl Woll

65.6k285171

answered 6 hours ago

Carl Woll

65.6k285171

answered 6 hours ago

Carl Woll

65.6k285171

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

add a comment |

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

What are UpValues and DownValues? The definition in the doc seems recursive: UpValue "gives a list of transformation rules corresponding to all upvalues defined for the symbol f. "
– R zu
6 hours ago

@Rzu Maybe you can check out the documentation for UpSetDelayed and TagSetDelayed.
– Carl Woll
6 hours ago

add a comment |

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