def sigmoid(Z):
    A = 1/(1+np.exp(-Z))
    cache = Z
    return A, cache


def relu(Z):
    A = np.maximum(0,Z)
    cache = Z 
    return A, cache


def tanh(Z):
    A = (np.exp(Z)-np.exp(-Z))/(np.exp(Z)+np.exp(-Z))
    cache = Z 
    return A, cache


def relu_backward(dA, Z):
    dZ = np.array(dA, copy=True) # just converting dz to a correct object.
    # When z <= 0, you should set dz to 0 as well. 
    dZ[Z <= 0] = 0
    return dZ

def sigmoid_backward(dA, Z):
    s = 1/(1+np.exp(-Z))
    dZ = dA * s * (1-s)
    return dZ

def tanh_backward(dA, Z):
    a, cache = tanh(Z)
    dZ = dA * (1-a**2)
    return dZ