diff --git a/GPy/kern/_src/prod.py b/GPy/kern/_src/prod.py
index bb809356..b324eaa7 100644
--- a/GPy/kern/_src/prod.py
+++ b/GPy/kern/_src/prod.py
@@ -39,17 +39,17 @@ class Prod(Kern):
         return self.k1.Kdiag(X[:,self.slice1]) * self.k2.Kdiag(X[:,self.slice2])
 
     def update_gradients_full(self, dL_dK, X):
-        self.k1.update_gradients_full(dL_dK*self.k2(X[:,self.slice2]), X[:,self.slice1])
-        self.k2.update_gradients_full(dL_dK*self.k1(X[:,self.slice1]), X[:,self.slice2])
+        self.k1.update_gradients_full(dL_dK*self.k2.K(X[:,self.slice2]), X[:,self.slice1])
+        self.k2.update_gradients_full(dL_dK*self.k1.K(X[:,self.slice1]), X[:,self.slice2])
 
     def gradients_X(self, dL_dK, X, X2=None):
         target = np.zeros(X.shape)
         if X2 is None:
-            target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2(X[:,self.slice2]), X[:,self.slice1], None)
-            target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1(X[:,self.slice1]), X[:,self.slice2], None)
+            target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2.K(X[:,self.slice2]), X[:,self.slice1], None)
+            target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1.K(X[:,self.slice1]), X[:,self.slice2], None)
         else:
-            target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2(X[:,self.slice2], X2[:,self.slice2]), X[:,self.slice1], X2[:,self.slice1])
-            target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1(X[:,self.slice1], X2[:,self.slice1]), X[:,self.slice2], X2[:,self.slice2])
+            target[:,self.slice1] += self.k1.gradients_X(dL_dK*self.k2.K(X[:,self.slice2], X2[:,self.slice2]), X[:,self.slice1], X2[:,self.slice1])
+            target[:,self.slice2] += self.k2.gradients_X(dL_dK*self.k1.K(X[:,self.slice1], X2[:,self.slice1]), X[:,self.slice2], X2[:,self.slice2])
         return target
 
     def gradients_X_diag(self, dL_dKdiag, X):