Simplify Derivative with Substitution
up vote
3
down vote
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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 yesterday
R zu
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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]]
calculus-and-analysis simplifying-expressions
asked yesterday
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 |
up vote
3
down vote
favorite
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]]
calculus-and-analysis simplifying-expressions
asked yesterday
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.
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
calculus-and-analysis simplifying-expressions
asked yesterday
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.
asked yesterday
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.
asked yesterday
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.
asked yesterday
R zu
1797
asked yesterday
R zu
1797
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.
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.
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 |
add a comment |
2 Answers
2
active
oldest
votes
up vote
7
down vote
accepted
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered yesterday
kglr
172k8194399
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
add a comment |
up vote
4
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]
1/u[x, y, z]
answered yesterday
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
yesterday
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
– Carl Woll
yesterday
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
7
down vote
accepted
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered yesterday
kglr
172k8194399
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
add a comment |
up vote
7
down vote
accepted
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered yesterday
kglr
172k8194399
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
add a comment |
up vote
7
down vote
accepted
up vote
7
down vote
accepted
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered yesterday
kglr
172k8194399
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered yesterday
kglr
172k8194399
edited yesterday
answered yesterday
kglr
172k8194399
answered yesterday
kglr
172k8194399
answered yesterday
kglr
172k8194399
172k8194399
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
add a comment |
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]– R zu
yesterday
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]– R zu
yesterday
@Rzu, good point.
– kglr
yesterday
@Rzu, good point.
– kglr
yesterday
add a comment |
up vote
4
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]
1/u[x, y, z]
answered yesterday
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
yesterday
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
– Carl Woll
yesterday
add a comment |
up vote
4
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]
1/u[x, y, z]
answered yesterday
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
yesterday
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
– Carl Woll
yesterday
add a comment |
up vote
4
down vote
up vote
4
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]
1/u[x, y, z]
answered yesterday
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]
1/u[x, y, z]
answered yesterday
Carl Woll
65.6k285171
answered yesterday
Carl Woll
65.6k285171
answered yesterday
Carl Woll
65.6k285171
answered yesterday
Carl Woll
65.6k285171
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
yesterday
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
– Carl Woll
yesterday
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
yesterday
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
– Carl Woll
yesterday
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
yesterday
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
yesterday
@Rzu Maybe you can check out the documentation for
UpSetDelayed and TagSetDelayed.– Carl Woll
yesterday
@Rzu Maybe you can check out the documentation for
UpSetDelayed and TagSetDelayed.– Carl Woll
yesterday
add a comment |
R zu is a new contributor. Be nice, and check out our Code of Conduct.
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