diff --git a/demo.typ b/demo.typ
index bbf1856..83d05d8 100644
--- a/demo.typ
+++ b/demo.typ
@@ -29,7 +29,7 @@ Set((x, y), pdv(f,x,y,[2,1]) + pdv(f,x,y,[1,2]) < epsilon) \
 quad
 ket(n^((1))) = sum_(k in.not D) mel(k^((0)), V, n^((0))) / (E_n^((0)) - E_k^((0))) ket(k^((0))),
 quad
-integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0 \
+integral_V dd(V) (pdv(cal(L), phi) - partial_mu (pdv(cal(L), (partial_mu phi)))) = 0 \
 
 dd(s,2) = -(1-(2G M)/r) dd(t,2) + (1-(2G M)/r)^(-1) dd(r,2) + r^2 dd(Omega,2)
 $
diff --git a/physica-manual.pdf b/physica-manual.pdf
index df43e15..b5db9af 100644
Binary files a/physica-manual.pdf and b/physica-manual.pdf differ
diff --git a/physica-manual.typ b/physica-manual.typ
index c57913a..ac3ab98 100644
--- a/physica-manual.typ
+++ b/physica-manual.typ
@@ -485,7 +485,7 @@ xmat(2, 2, #g)`)
   [`matrixelement(`..`)`],
   [`mel`],
   [
-    `mel(n, diff_nu H, m)` \ #sym.arrow $mel(n, diff_nu H, m)$
+    `mel(n, partial_nu H, m)` \ #sym.arrow $mel(n, partial_nu H, m)$
   ],
   [matrix element, same as `braket(n,M,n)`],
 )
@@ -753,7 +753,7 @@ Function: `partialderivative(`_f_, \*_args_, \*\*_kwargs_`)`, abbreviated as `pd
 - _f_: the function, which can be `#none` or omitted,
 - positional _args_: the variable names, *optionally* followed by an order number e.g. `2`, or an order array e.g. `[2,3]`, `[k]`, `[m n, lambda+1]`.
 - named _kwargs_:
-  - `d`: the differential symbol [default: `diff`].
+  - `d`: the differential symbol [default: `partial`].
   - `s`: the "slash" separating the numerator and denominator [default: `none`], by default it produces the normal fraction form $pdv(f,x)$. The most common non-default is `slash` or simply `\/`, so as to create a flat form $pdv(f,x,s:\/)$ that fits inline.
   - `total`: the user-specified total order.
     - If it is absent, then (1) if the orders assigned to all variables are numeric, the total order number will be *automatically computed*; (2) if non-number symbols are present, computation will be attempted with minimum effort, and a user override with argument `total` may be necessary.
@@ -821,8 +821,8 @@ Function: `partialderivative(`_f_, \*_args_, \*\*_kwargs_`)`, abbreviated as `pd
   ]
 )
 
-*(13)* #hl(`integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0`) \
-$ integral_V dd(V) (pdv(cal(L), phi) - diff_mu (pdv(cal(L), (diff_mu phi)))) = 0 $
+*(13)* #hl(`integral_V dd(V) (pdv(cal(L), phi) - partial_mu (pdv(cal(L), (partial_mu phi)))) = 0`) \
+$ integral_V dd(V) (pdv(cal(L), phi) - partial_mu (pdv(cal(L), (partial_mu phi)))) = 0 $
 
 == Special show rules
 
@@ -1057,8 +1057,8 @@ Function: `tensor(`_symbol_, \*_args_`)`.
   ],
 )
 
-*(9)* `grad_mu A^nu = diff_mu A^nu + tensor(Gamma,+nu,-mu,-lambda) A^lambda`
-$ grad_mu A^nu = diff_mu A^nu + tensor(Gamma,+nu,-mu,-lambda) A^lambda $
+*(9)* `grad_mu A^nu = partial_mu A^nu + tensor(Gamma,+nu,-mu,-lambda) A^lambda`
+$ grad_mu A^nu = partial_mu A^nu + tensor(Gamma,+nu,-mu,-lambda) A^lambda $
 
 === Isotopes
 
diff --git a/physica.typ b/physica.typ
index 263c26b..710653a 100644
--- a/physica.typ
+++ b/physica.typ
@@ -345,7 +345,7 @@
   assert(type(xs) == array, message: "expecting an array of variable names")
   let arrays = ()  // array of arrays
   for f in fs {
-    arrays.push(xs.map((x) => __mate(math.frac($diff#f$, $diff#x$), big)))
+    arrays.push(xs.map((x) => __mate(math.frac($partial#f$, $partial#x$), big)))
   }
   math.mat(delim: delim, ..arrays)
 }
@@ -364,8 +364,8 @@
     for c in range(order) {
       let xc = xs.at(c)
       row_array.push(__mate(math.frac(
-        $diff^2 #f$,
-        if xr == xc { $diff #xr^2$ } else { $diff #xr diff #xc$ }
+        $partial^2 #f$,
+        if xr == xc { $partial #xr^2$ } else { $partial #xr partial #xc$ }
       ), big))
     }
     row_arrays.push(row_array)
@@ -693,7 +693,7 @@
     __bare_minimum_effort_symbolic_add(orders)
   }
 
-  let d = kwargs.at("d", default: $diff$)
+  let d = kwargs.at("d", default: $partial$)
   
   let lowers = ()
   for i in range(var_num) {