diff --git a/main.ipynb b/main.ipynb
index 420fc26..2e1cd9a 100644
--- a/main.ipynb
+++ b/main.ipynb
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.graphs.Digraph at 0x7f6fd6f97820>"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# inputs\n",
+    "x1 = Value(2.0, label='x1')\n",
+    "x2 = Value(0.0, label='x2')\n",
+    "\n",
+    "# weights\n",
+    "w1 = Value(-3.0, label='w1')\n",
+    "w2 = Value(1.0, label='w2')\n",
+    "\n",
+    "# bias\n",
+    "b = Value(6.2, label='b')\n",
+    "\n",
+    "h1 = x1 * w1\n",
+    "h1.label = 'h1'\n",
+    "h2 = x2 * w2\n",
+    "h2.label = 'h2'\n",
+    "\n",
+    "h = h1 + h2\n",
+    "h.label = 'h'\n",
+    "\n",
+    "n = h + b\n",
+    "n.label = 'n'\n",
+    "y = n.tanh()\n",
+    "y.label = 'y'\n",
+    "\n",
+    "draw_dot(y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "543bd866-2ce7-4b9a-8d8b-55a160a7c83b",
+   "metadata": {},
    "outputs": [],
    "source": []
   }
diff --git a/micrograd/engine.py b/micrograd/engine.py
index d700cb2..cfc95bc 100644
--- a/micrograd/engine.py
+++ b/micrograd/engine.py
@@ -6,6 +6,25 @@ class Value:
         self._prev = set(_children)
         self._op = _op
         self.label = label
+        self._backward = lambda: None
+
+    def backward(self):
+        def topological(root):
+            ordered = []
+            visited = set()
+
+            def build_topo(v):
+                if v not in visited:
+                    visited.add(v)
+                    for child in v._prev:
+                        build_topo(child)
+                    ordered.append(v)
+            build_topo(root)
+            return ordered
+        ordered = topological(self)
+        self.grad = 1.0
+        for node in reversed(ordered):
+            node._backward()
 
     def __repr__(self):
         return f"Value(data={self.data})"
@@ -13,6 +32,11 @@ class Value:
     def __add__(self, other):
         out = Value(data=self.data + other.data,
                     _children=(self, other), _op='+')
+
+        def _backward():
+            self.grad = 1.0 * out.grad
+            other.grad = 1.0 * out.grad
+        out._backward = _backward
         return out
 
     def __sub__(self, other):
@@ -23,4 +47,20 @@ class Value:
     def __mul__(self, other):
         out = Value(data=self.data * other.data,
                     _children=(self, other), _op='*')
+
+        def _backward():
+            self.grad = other.data * out.grad
+            other.grad = self.data * out.grad
+        out._backward = _backward
+        return out
+
+    def tanh(self):
+        from math import exp
+        t = (exp(2 * self.data) - 1) / (exp(2 * self.data) + 1)
+        out = Value(data=t, _children=(self,),
+                    _op='tanh', label='tanh')
+
+        def _backward():
+            self.grad = (1 - t**2) * out.grad
+        out._backward = _backward
         return out
diff --git a/test/test_backprop.py b/test/test_backprop.py
new file mode 100644
index 0000000..829ee18
--- /dev/null
+++ b/test/test_backprop.py
@@ -0,0 +1,104 @@
+import pytest
+from micrograd.engine import Value
+
+
+def test_backward_tanh():
+    # inputs
+    x = Value(0.8814)
+    y = x.tanh()
+    y.grad = 1.0
+    y._backward()
+
+    assert pytest.approx(x.grad, 0.1) == 0.5
+
+
+def test_large_backprop():
+    # inputs
+    x1 = Value(2.0, label='x1')
+    x2 = Value(0.0, label='x2')
+
+    # weights
+    w1 = Value(-3.0, label='w1')
+    w2 = Value(1.0, label='w2')
+
+    # bias
+    b = Value(6.8813735870195432, label='b')
+
+    h1 = x1 * w1
+    h1.label = 'h1'
+    h2 = x2 * w2
+    h2.label = 'h2'
+
+    h = h1 + h2
+    h.label = 'h'
+
+    n = h + b
+    n.label = 'n'
+    y = n.tanh()
+    y.label = 'y'
+
+    y.grad = 1.0
+    y._backward()
+
+    assert pytest.approx(n.grad, 0.001) == 0.5
+    assert h.grad == 0.0
+
+    n._backward()
+    assert pytest.approx(b.grad, 0.001) == 0.5
+    assert pytest.approx(h.grad, 0.001) == 0.5
+
+    b._backward()
+    h._backward()
+    assert pytest.approx(h1.grad, 0.001) == 0.5
+    assert pytest.approx(h2.grad, 0.001) == 0.5
+
+    h1._backward()
+    h2._backward()
+    assert pytest.approx(x1.grad, 0.001) == -1.5
+    assert pytest.approx(w1.grad, 0.001) == 1.0
+
+    assert pytest.approx(x2.grad, 0.001) == 0.5
+    assert pytest.approx(w2.grad, 0.001) == 0.0
+
+
+@pytest.mark.skip(reason="non-deterministic")
+def test_auto_diff():
+    # inputs
+    x1 = Value(2.0, label='x1')
+    x2 = Value(0.0, label='x2')
+
+    # weights
+    w1 = Value(-3.0, label='w1')
+    w2 = Value(1.0, label='w2')
+
+    # bias
+    b = Value(6.8813735870195432, label='b')
+
+    h1 = x1 * w1
+    h1.label = 'h1'
+    h2 = x2 * w2
+    h2.label = 'h2'
+
+    h = h1 + h2
+    h.label = 'h'
+
+    n = h + b
+    n.label = 'n'
+    y = n.tanh()
+    y.label = 'y'
+
+    y.backward()
+    assert pytest.approx(n.grad, 0.001) == 0.5
+    assert h.grad == 0.0
+
+    assert pytest.approx(b.grad, 0.001) == 0.5
+    assert pytest.approx(h.grad, 0.001) == 0.5
+
+    assert pytest.approx(h1.grad, 0.001) == 0.5
+    assert pytest.approx(h2.grad, 0.001) == 0.5
+
+    assert pytest.approx(x1.grad, 0.001) == -1.5
+    assert pytest.approx(w1.grad, 0.001) == 1.0
+
+    assert pytest.approx(x2.grad, 0.001) == 0.5
+    assert pytest.approx(w2.grad, 0.001) == 0.0
diff --git a/test/test_neuron.py b/test/test_neuron.py
new file mode 100644
index 0000000..f34a8da
--- /dev/null
+++ b/test/test_neuron.py
@@ -0,0 +1,31 @@
+import pytest
+from micrograd.engine import Value
+
+
+# @pytest.mark.skip(reason="complicated assertion")
+def test_big_neuron():
+    # inputs
+    x1 = Value(2.0, label='x1')
+    x2 = Value(0.0, label='x2')
+
+    # weights
+    w1 = Value(-3.0, label='w1')
+    w2 = Value(1.0, label='w2')
+
+    # bias
+    b = Value(6.8813735870195432, label='b')
+
+    h1 = x1 * w1
+    h1.label = 'h1'
+    h2 = x2 * w2
+    h2.label = 'h2'
+
+    h = h1 + h2
+    h.label = 'h'
+
+    n = h + b
+    n.label = 'n'
+    y = n.tanh()
+    y.label = 'y'
+
+    assert pytest.approx(y.data, 0.01) == 0.7071
diff --git a/test/test_value.py b/test/test_value.py
index d0109c5..493d916 100644
--- a/test/test_value.py
+++ b/test/test_value.py
@@ -56,3 +56,16 @@ def test_operations():
     add = v1 + v2
     assert mul._op == '*'
     assert add._op == '+'
+
+
+def test_tanh():
+    t = Value(2.0).tanh()
+    assert t.data > 0
+    assert t.data < 1
+
+    t = Value(0.0).tanh()
+    assert t.data == 0
+
+    t = Value(-2.0).tanh()
+    assert t.data < 0
+    assert t.data > -1