import math

def sigmoid(x):
    return 1.0 / (1.0 + math.exp(-x))

def sigmoid_prime(x): # x already sigmoided
    return x * (1 - x)

def relu(x):
    return max(0,x)

def relu_prime(x):
    return 1 if x>0 else 0

def tanh(x):
    return math.tanh(x)

def tanh_prime(x):
    return 1 - x**2

def softmax(x):
    return math.exp(x) / (math.exp(x) + 1)

def softmax_prime(x):
    return x * (1 - x)