Creating cost function and gradient for gradient descent

Since I started to learn Machine Learning, it is important to fully understand the algorithms. Therefore, I will implement ML algorithms from scratch and compare them with the implementation of scikit-learn library.

To start, I created functions for the gradient descent algorithm.

Here is the cost J(w, b).

And these are partial derivatives.

import math, copy
import numpy as np
x_train = np.array([1.0, 2.0, 3.0])   #features
y_train = np.array([300.0, 500.0, 700.0])   #target value
#I am going to create a cost function, which shows how different cost function and actual value is.
#This cost function can calculate how much difference there is when you use a certain w and b.
#This returns J(w, b)

def compute_cost(x, y, w, b):
    m = x.shape[0] #The length of the array
    cost =0

    for i in range(m):
        f_wb = w*x[i]+b
        cost += (f_wb-y[i])**2
    total_cost = 1/(2*m)*cost

    return total_cost
#Next, this is the calculation of gradient. If you calculate the partial derivative of J(w, b). 
def compute_gradient(x, y, w, b):
    m=x.shape[0]
    dj_dw = 0
    dj_db = 0

    for i in range(m):
        f_wb = w*x[i]+b
        dj_dw_i = (f_wb - y[i]) * x[i]
        dj_db_i = f_wb - y[i] 
        dj_db += dj_db_i
        dj_dw += dj_dw_i

    dj_dw = dj_dw / m 
    dj_db = dj_db / m 

    return dj_dw, dj_db