diff --git a/src/emmy/calculus/derivative.cljc b/src/emmy/calculus/derivative.cljc
index 53c1a742..f189ffb4 100644
--- a/src/emmy/calculus/derivative.cljc
+++ b/src/emmy/calculus/derivative.cljc
@@ -22,9 +22,8 @@
 
 ;; ## Single and Multivariable Calculus
 ;;
-;; These functions put together the pieces laid out
-;; in [[emmy.dual]] and declare an interface for taking
-;; derivatives.
+;; These functions put together the pieces laid out in [[emmy.dual]] and declare
+;; an interface for taking derivatives.
 
 ;; The result of applying the derivative `(D f)` of a multivariable function `f`
 ;; to a sequence of `args` is a structure of the same shape as `args` with all
@@ -70,6 +69,8 @@
            " at path " path
            " in input structure " structure)))))
 
+;; TODO have this jacobian be its own thing, then augment it with multi.
+
 (defn- jacobian
   "Takes:
 
@@ -108,6 +109,8 @@
        ;; correctly into the supplied `input`, triggering this exception.
        (u/illegal (str "Bad selectors " selectors " for structure " input))))))
 
+;; TODO can we do something like this for gradient, with gradient in both slots??
+
 (defn- euclidean
   "Slightly more general version of [[jacobian]] that can handle a single
   non-structural input; dispatches to either [[jacobian]] or [[derivative]]
@@ -143,6 +146,15 @@
               (str "Selectors " selectors
                    " not allowed for non-structural input " input)))))))
 
+(defn multi [op f]
+  (-> (fn
+        ([] 0)
+        ([x] ((op f) x))
+        ([x & more]
+         ((multi op (fn [xs] (apply f xs)))
+          (matrix/seq-> (cons x more)))))
+      (f/with-arity (f/arity f) {:from ::multi})))
+
 (defn- multivariate
   "Slightly wider version of [[euclidean]]. Accepts:
 
@@ -161,15 +173,13 @@
   Single-argument functions don't transform their arguments."
   ([f] (multivariate f []))
   ([f selectors]
-   (let [d #(euclidean % selectors)
-         df (d f)
-         df* (d (fn [args] (apply f args)))]
-     (-> (fn
-           ([] 0)
-           ([x] (df x))
-           ([x & more]
-            (df* (matrix/seq-> (cons x more)))))
-         (f/with-arity (f/arity f) {:from ::multivariate})))))
+   (let [d #(euclidean % selectors)]
+     (multi d f))))
+
+(defn gradient
+  ([f] (gradient f []))
+  ([f selectors]
+   (multi #(tape/gradient % selectors) f)))
 
 ;; ## Generic [[g/partial-derivative]] Installation
 ;;
@@ -197,19 +207,42 @@
 ;; implementation for the components. I vote to back out this `::s/structure`
 ;; installation.
 
+(def ^:dynamic *mode* d/FORWARD-MODE)
+
 (doseq [t [::v/function ::s/structure]]
   (defmethod g/partial-derivative [t v/seqtype] [f selectors]
-    (multivariate f selectors))
+    (if (= *mode* d/FORWARD-MODE)
+      (multivariate f selectors)
+      (gradient f selectors)))
 
   (defmethod g/partial-derivative [t nil] [f _]
-    (multivariate f [])))
+    (if (= *mode* d/FORWARD-MODE)
+      (multivariate f [])
+      (gradient f []))))
 
 ;; ## Operators
 ;;
 ;; This section exposes various differential operators as [[o/Operator]]
 ;; instances.
 
-(def D
+(def ^{:arglists '([f])}
+  D-forward
+  (o/make-operator
+   (fn [x]
+     (binding [*mode* d/FORWARD-MODE]
+       (g/partial-derivative x [])))
+   g/derivative-symbol))
+
+(def ^{:arglists '([f])}
+  D-reverse
+  (o/make-operator
+   (fn [x]
+     (binding [*mode* d/REVERSE-MODE]
+       (g/partial-derivative x [])))
+   g/derivative-symbol))
+
+(def ^{:arglists '([f])}
+  D
   "Derivative operator. Takes some function `f` and returns a function whose value
   at some point can multiply an increment in the arguments to produce the best
   linear estimate of the increment in the function value.
@@ -222,8 +255,7 @@
   The related [[emmy.env/Grad]] returns a function that produces a structure of
   the opposite orientation as [[D]]. Both of these functions use forward-mode
   automatic differentiation."
-  (o/make-operator #(g/partial-derivative % [])
-                   g/derivative-symbol))
+  D-forward)
 
 (defn D-as-matrix [F]
   (fn [s]
@@ -232,13 +264,28 @@
      ((D F) s)
      s)))
 
-(defn partial
+(defn partial-forward
+  [& selectors]
+  (o/make-operator
+   (fn [x]
+     (binding [*mode* d/FORWARD-MODE]
+       (g/partial-derivative x selectors)))
+   `(~'partial ~@selectors)))
+
+(defn partial-reverse
+  [& selectors]
+  (o/make-operator
+   (fn [x]
+     (binding [*mode* d/REVERSE-MODE]
+       (g/partial-derivative x selectors)))
+   `(~'partial ~@selectors)))
+
+(def ^{:arglists '([& selectors])}
+  partial
   "Returns an operator that, when applied to a function `f`, produces a function
   that computes the partial derivative of `f` at the (zero-based) slot index
   provided via `selectors`."
-  [& selectors]
-  (o/make-operator #(g/partial-derivative % selectors)
-                   `(~'partial ~@selectors)))
+  partial-forward)
 
 ;; ## Derivative Utilities
 ;;
diff --git a/test/emmy/calculus/derivative_test.cljc b/test/emmy/calculus/derivative_test.cljc
index ceb935e8..c76075dd 100644
--- a/test/emmy/calculus/derivative_test.cljc
+++ b/test/emmy/calculus/derivative_test.cljc
@@ -1616,9 +1616,6 @@
           "symbolic-taylor-series keeps the arguments symbolic, even when they
           are numbers."))))
 
-;; TODO enable when we add our gradient impl in the next PR.
-
-#_
 (deftest mixed-mode-tests
   (testing "multiple input, vector output"
     (let [f (fn [a b c d e f]
@@ -1686,3 +1683,7 @@
 
 (deftest forward-mode-tests
   (all-tests d/D d/partial))
+
+(deftest reverse-mode-tests
+  (all-tests d/D-reverse
+             d/partial-reverse))