diff --git a/network.py b/network.py
index bb2a49d..3c1aade 100644
--- a/network.py
+++ b/network.py
@@ -94,8 +94,8 @@ class Model(object):
     def dLdb2(self, x, y):
         return self.dLdf(x, y) * self.dfdb2()
 
-    def dfdw2(self, x):
-        return np.sum(self.a(x))
+    def dfdw2(self, x):  # how each entry of f changes wrt each entry of w2
+        return self.a(x)
 
     def dfda(self):  # how f changes with ith element of a
         return self.w2
@@ -106,10 +106,10 @@ class Model(object):
 
     def dLdz1(self, x, y):
         """Compute dL/dz1 for an input x and expected output y"""
-        return self.dLdf(x, y) * np.sum(self.dfda() * self.dadz1(x))
+        return self.dLdf(x, y) * np.dot(self.dfda(), self.dadz1(x))
 
     def dz1dw1(self, x):
-        return x
+        return x * self.w1
 
     def dLdw1(self, x, y):
         """Compute dL/dw1 for an input x and expected output y"""