Derivative Functions

import numpy as np

def find_term_derivative(term):
    constant = term[0]*term[1]
    exponent = term[1] - 1
    return (constant, exponent)

def find_derivative(function_terms):
    derivative_terms = list(map(lambda term: find_term_derivative(term),function_terms))
    return list(filter(lambda derivative_term: derivative_term[0] != 0, derivative_terms))
def term_output(term, input_value):
    return term[0]*input_value**term[1]

def output_at(list_of_terms, x_value):
    outputs = list(map(lambda term: term_output(term, x_value), list_of_terms))
    return sum(outputs)

def derivative_at(terms, x):
    derivative_fn = find_derivative(terms)
    total = 0
    for term in derivative_fn:
        total += term[0]*x**term[1]
    return total


def errors(x_values, y_values, m, b):
    y_line = (b + m*x_values)
    return (y_values - y_line)

def squared_errors(x_values, y_values, m, b):
    return errors(x_values, y_values, m, b)**2

def residual_sum_squares(x_values, y_values, m, b):
    return sum(squared_errors(x_values, y_values, m, b))

def slope_at(x_values, y_values, m, b):
    delta = .001
    base_rss = residual_sum_squares(x_values, y_values, m, b)
    delta_rss = residual_sum_squares(x_values, y_values, m, b + delta)
    numerator = delta_rss - base_rss
    slope = numerator/delta
    return {'b': b, 'slope': slope}
    
def gradient_descent(x_values, y_values, steps, current_b, learning_rate, m):
    cost_curve = []
    for i in range(steps):
        current_cost_slope = slope_at(x_values, y_values, m, current_b)['slope']
        current_rss = residual_sum_squares(x_values, y_values, m, current_b)
        cost_curve.append({'b': current_b, 'rss': round(current_rss,2), 'slope': round(current_cost_slope,2)})
        current_b = updated_b(current_b, learning_rate, current_cost_slope)
    return cost_curve