Simplify Derivative with Substitution
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I try to evaluate:
$$ fracpartialpartial x logu(x, y, z)$$
Mathematica gives:
$$ frac1x+y+z$$
I want to simplify the expression with my function:
$$ frac1u(x, y, z)$$
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
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up vote
3
down vote
favorite
I try to evaluate:
$$ fracpartialpartial x logu(x, y, z)$$
Mathematica gives:
$$ frac1x+y+z$$
I want to simplify the expression with my function:
$$ frac1u(x, y, z)$$
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
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I try to evaluate:
$$ fracpartialpartial x logu(x, y, z)$$
Mathematica gives:
$$ frac1x+y+z$$
I want to simplify the expression with my function:
$$ frac1u(x, y, z)$$
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
I try to evaluate:
$$ fracpartialpartial x logu(x, y, z)$$
Mathematica gives:
$$ frac1x+y+z$$
I want to simplify the expression with my function:
$$ frac1u(x, y, z)$$
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 Nov 22 at 17:33
R zu
1797
1797
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2 Answers
2
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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]
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
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]
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation forUpSetDelayed
andTagSetDelayed
.
– Carl Woll
Nov 22 at 19:39
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]
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
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]
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
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]
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
edited Nov 22 at 18:05
answered Nov 22 at 17:36
kglr
173k8196401
173k8196401
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
add a comment |
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]
– R zu
Nov 22 at 18:04
@Rzu, good point.
– kglr
Nov 22 at 18:05
@Rzu, good point.
– kglr
Nov 22 at 18:05
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]
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation forUpSetDelayed
andTagSetDelayed
.
– Carl Woll
Nov 22 at 19:39
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]
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation forUpSetDelayed
andTagSetDelayed
.
– Carl Woll
Nov 22 at 19:39
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]
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 Nov 22 at 19:26
Carl Woll
65.9k285171
65.9k285171
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation forUpSetDelayed
andTagSetDelayed
.
– Carl Woll
Nov 22 at 19:39
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation forUpSetDelayed
andTagSetDelayed
.
– Carl Woll
Nov 22 at 19:39
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
Nov 22 at 19:29
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
Nov 22 at 19:29
@Rzu Maybe you can check out the documentation for
UpSetDelayed
and TagSetDelayed
.– Carl Woll
Nov 22 at 19:39
@Rzu Maybe you can check out the documentation for
UpSetDelayed
and TagSetDelayed
.– Carl Woll
Nov 22 at 19:39
add a comment |
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