diff --git a/README.md b/README.md
index 071f75d..3303f98 100644
--- a/README.md
+++ b/README.md
@@ -32,7 +32,7 @@ See the [manual](https://github.com/Leedehai/typst-physics/blob/master/physica-m
 
 A larger [demo.typ](https://github.com/Leedehai/typst-physics/blob/master/demo.typ):
 
-![demo-larger](https://github.com/Leedehai/typst-physics/assets/18319900/af4fcf6c-5da3-48d1-a7a7-59053f808db5)
+![demo-larger](https://github.com/Leedehai/typst-physics/assets/18319900/b7dadf90-b401-4bbb-aff7-7c8840954209)
 
 ## Using physica in your Typst document
 
diff --git a/demo.typ b/demo.typ
index f5b38f0..bbf1856 100644
--- a/demo.typ
+++ b/demo.typ
@@ -11,7 +11,7 @@ A^T, curl vb(E) = - pdv(vb(B), t),
 quad
 tensor(Lambda,+mu,-nu) = dmat(1,RR),
 quad
-dd(x,y),
+f(x,y) dd(x,y),
 quad
 dd(vb(x),y,[3]),
 quad
diff --git a/physica-manual.pdf b/physica-manual.pdf
index a85543e..feaa1af 100644
Binary files a/physica-manual.pdf and b/physica-manual.pdf differ
diff --git a/physica-manual.typ b/physica-manual.typ
index ee2270a..a9b9f46 100644
--- a/physica-manual.typ
+++ b/physica-manual.typ
@@ -165,7 +165,7 @@ All symbols need to be used in *math mode* `$...$`.
   [`TT`],
   [],
   [`v^TT, A^TT` #sym.arrow $v^TT, A^TT$],
-  [transpose, also see\ @matrix-tranpose],
+  [transpose, also see\ @matrix-transpose],
 
   [`vectorbold(`_content_`)`],
   [`vb`],
@@ -234,7 +234,7 @@ All symbols need to be used in *math mode* `$...$`.
   [`TT`],
   [],
   [`v^TT, A^TT` #sym.arrow $v^TT, A^TT$],
-  [transpose, also see\ @matrix-tranpose],
+  [transpose, also see\ @matrix-transpose],
 
   [#builtin([`mat(`...`)`])],
   [],
@@ -592,6 +592,14 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
   - `d`: the differential symbol [default: `upright(d)`].
   - `p`: the product symbol connecting the components [default: `none`].
 
+TeXBook advises _[f]ormulas involving calculus look best when an extra thin space
+appears before dx or dy or d whatever_ (Chapter 18 p.168), and this package
+heeds this advice. If you don't want the spaces between the d-units, you may set
+in a `compact:#true` argument: $dd(r,theta) "vs." dd(r,theta,compact:#true)$ (compact).
+// https://github.com/typst/typst/issues/147 advocates for set rules for
+// non built-in functions. When that's implemented, user can do a
+// #set dd(compact: true) to set this param for all dd() invocations.
+
 *Order assignment algorithm:*
 - If there is no order number or order array, all variables has order 1.
 - If there is an order number (not an array), then this order number is assigned to _every_ variable, e.g. `dd(x,y,2)` assigns $x <- 2, y <- 2$.
@@ -607,8 +615,8 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
   column-gutter: 2em,
 
   [
-    *(1)* #hl(`dd(f), dd(x,y)`) \
-    $ dd(f), dd(x,y) $
+    *(1)* #hl(`dd(f), f(r,theta) dd(r,theta)`) \
+    $ dd(f), f(r,theta) dd(r,theta) $
   ],
   [
     *(2)* #hl(`dd(x,3), dd(f,[k]), dd(f,[k],d:delta)`) \
@@ -619,8 +627,8 @@ Functions: `differential(`\*_args_, \*\*_kwargs_`)`, abbreviated as `dd(`...`)`.
     $ dd(f,2), dd(vb(x),t,[3,]) $
   ],
   [
-    *(4)* #hl(`dd(x,y,[2,3]), dd(x,y,z,[2,3])`) \
-    $ dd(x,y,[2,3]), dd(x,y,z,[2,3]) $
+    *(4)* #hl(`dd(x,y), dd(x,y,[2,3]), dd(x,y,z,[2,3])`) \
+    $ dd(x,y), dd(x,y,[2,3]), dd(x,y,z,[2,3]) $
   ],
   [
     *(5)* #hl(`dd(x, y, z, [[1,1],rho+1,n_1])`) \
@@ -785,7 +793,7 @@ In the default font, the Typst built-in symbol `planck.reduce` $planck.reduce$ l
   [$ i hbar pdv(,t) psi = -frac(hbar^2, 2m) laplacian psi $],
 )
 
-=== Matrix transpose with superscript T <matrix-tranpose>
+=== Matrix transpose with superscript T <matrix-transpose>
 
 #v(1em)
 
diff --git a/physica.typ b/physica.typ
index 7f3ff2a..f0e3895 100644
--- a/physica.typ
+++ b/physica.typ
@@ -465,7 +465,11 @@
   }
 
   let dsym = kwargs.at("d", default: $upright(d)$)
-  let prod = kwargs.at("p", default: none)
+  let compact = kwargs.at("compact", default: false)
+  // Why a very thin space is the default joiner: see TeXBook Chapter 18 p.168.
+  // math.thin is 1/6 em, and I decide this very thin space shall be slightly
+  // more than half of that.
+  let prod = kwargs.at("p", default: if compact { none } else { h(0.09em) })
 
   let difference = var_num - orders.len()
   while difference > 0 {
@@ -482,7 +486,10 @@
       arr.push($dsym#var$)
     }
   }
-  $#arr.join(prod)$
+  // Wrap in op(...) to give it smart spacing, just like Typst's built-in "dif"
+  // symbol. For example, there should be a space in the middle of "f(x) dx".
+  // See TeXBook Chapter 18 p.168.
+  $op(#arr.join(prod))$
 }
 #let dd = differential
 
diff --git a/typst.toml b/typst.toml
index 79ba0dc..c666474 100644
--- a/typst.toml
+++ b/typst.toml
@@ -8,9 +8,10 @@ keywords = [
   "physics", "mathematics", "brace", "set", "product", "evaluate", "restrict",
   "integral", "gradient", "divergence", "curl", "vector", "field", "laplacian",
   "matrix", "determinant", "diagonal", "identity", "Jacobian", "Hessian",
-  "Dirac", "braket", "differential", "derivative", "partial", "dv", "odv",
-  "pdv", "Planck", "hbar", "tensor", "isotope", "signal", "electromagnetism",
-  "mechanics", "quantum", "relativity", "imaginary", "notation",
+  "transpose", "Dirac", "braket", "differential", "derivative", "partial",
+  "dv", "odv", "pdv", "Planck", "hbar", "tensor", "isotope", "signal",
+  "electromagnetism", "mechanics", "quantum", "relativity", "imaginary",
+  "notation",
 ]
 compiler = "0.10.0"
 exclude = ["*.pdf", "*.py"]