Simplify Derivative with Substitution
3
$begingroup$
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 Nov 22 '18 at 17:33
R zuR zu
1847
$endgroup$
add a comment |
3
$begingroup$
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 Nov 22 '18 at 17:33
R zuR zu
1847
$endgroup$
add a comment |
3
3
3
$begingroup$
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 Nov 22 '18 at 17:33
R zuR zu
1847
$endgroup$
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 Nov 22 '18 at 17:33
R zuR zu
1847
asked Nov 22 '18 at 17:33
R zuR zu
1847
asked Nov 22 '18 at 17:33
R zuR zu
1847
asked Nov 22 '18 at 17:33
R zuR zu
1847
asked Nov 22 '18 at 17:33
R zuR zu
1847
1847
add a comment |
add a comment |
2 Answers
2
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oldest
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7
$begingroup$
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
$endgroup$
$begingroup$
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
add a comment |
4
$begingroup$
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 '18 at 19:26
Carl WollCarl Woll
67.5k389175
$endgroup$
$begingroup$
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. "
$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
7
$begingroup$
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
$endgroup$
$begingroup$
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
add a comment |
7
$begingroup$
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
$endgroup$
$begingroup$
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
add a comment |
7
7
7
$begingroup$
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
$endgroup$
D[Log[u[x, y, z]], x] /. u[x_, y_, z_] :> Defer[u[x, y, z]]
1/u[x, y, z]
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
edited Nov 22 '18 at 18:05
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
answered Nov 22 '18 at 17:36
kglrkglr
181k10200413
181k10200413
$begingroup$
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
add a comment |
$begingroup$
A more general substitution:/. u[x_,y_,z_] -> Defer[u[x,y,z]]
$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
$begingroup$
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
A more general substitution:
/. u[x_,y_,z_] -> Defer[u[x,y,z]]$endgroup$
– R zu
Nov 22 '18 at 18:04
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
$begingroup$
@Rzu, good point.
$endgroup$
– kglr
Nov 22 '18 at 18:05
add a comment |
4
$begingroup$
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 '18 at 19:26
Carl WollCarl Woll
67.5k389175
$endgroup$
$begingroup$
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. "
$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
add a comment |
4
$begingroup$
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 '18 at 19:26
Carl WollCarl Woll
67.5k389175
$endgroup$
$begingroup$
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. "
$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
add a comment |
4
4
4
$begingroup$
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 '18 at 19:26
Carl WollCarl Woll
67.5k389175
$endgroup$
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 '18 at 19:26
Carl WollCarl Woll
67.5k389175
answered Nov 22 '18 at 19:26
Carl WollCarl Woll
67.5k389175
answered Nov 22 '18 at 19:26
Carl WollCarl Woll
67.5k389175
answered Nov 22 '18 at 19:26
Carl WollCarl Woll
67.5k389175
67.5k389175
$begingroup$
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. "
$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
add a comment |
$begingroup$
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. "
$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation forUpSetDelayedandTagSetDelayed.
$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
$begingroup$
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. "$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
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. "$endgroup$
– R zu
Nov 22 '18 at 19:29
$begingroup$
@Rzu Maybe you can check out the documentation for
UpSetDelayed and TagSetDelayed.$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
$begingroup$
@Rzu Maybe you can check out the documentation for
UpSetDelayed and TagSetDelayed.$endgroup$
– Carl Woll
Nov 22 '18 at 19:39
add a comment |
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