diff --git a/functions.py b/functions.py
new file mode 100644
index 0000000..d77cf95
--- /dev/null
+++ b/functions.py
@@ -0,0 +1,87 @@
+import numpy as np
+
+
+class Relu:
+    @staticmethod
+    def activation(z):
+        z[z < 0] = 0
+        return z
+
+    @staticmethod
+    def prime(z):
+        z[z < 0] = 0
+        z[z > 0] = 1
+        return z
+
+
+class Sigmoid:
+    @staticmethod
+    def activation(z):
+        return 1 / (1 + np.exp(-z))
+
+    @staticmethod
+    def prime(z):
+        return Sigmoid.activation(z) * (1 - Sigmoid.activation(z))
+
+
+class Softmax:
+    @staticmethod
+    def activation(z):
+        """
+        https://stackoverflow.com/questions/34968722/softmax-function-python
+
+        Numerically stable version
+        """
+        e_x = np.exp(z - np.max(z))
+        return e_x / e_x.sum()
+
+    # https://stackoverflow.com/questions/33541930/how-to-implement-the-softmax-derivative-independently-from-any-loss-function
+    # http://cs231n.github.io/neural-networks-case-study/#loss
+
+
+class CrossEntropy:
+    """
+    Used with Softmax activation in final layer
+    """
+
+    @staticmethod
+    def activation(z):
+        return Softmax.activation(z)
+
+    @staticmethod
+    def delta(y_hat, y):
+        """
+        https://stackoverflow.com/questions/27089932/cross-entropy-softmax-and-the-derivative-term-in-backpropagation
+        :param y_hat: (array) One hot encoded truth vector.
+        :param y: (array) Prediction vector.
+        :return: (array) Delta vector.
+
+        y are softmax probabilitys
+        y_hat is truth vector one hot encoded
+
+        y         y_hat
+        [0.8]     [1]
+        [0.1]     [0]
+        [0.1]     [0]
+
+        result:
+
+        [-0.2]
+        [0.1]
+        [0.1]
+
+        """
+        return y - y_hat
+
+    @staticmethod
+    def loss(y_hat, y):
+        """
+        https://datascience.stackexchange.com/questions/9302/the-cross-entropy-error-function-in-neural-networks
+
+        :param y_hat: (array) One hot encoded truth vector.
+        :param y: (array) Prediction vector
+        :return: (flt)
+        """
+        return -np.dot(y_hat, np.log(y))
+
+