#!/usr/bin/env python
# coding: utf-8

# # Automatic Differentiation

# In[1]:


from mxnet import autograd, np, npx  
npx.set_np()

x = np.arange(4)
x


# Allocate space to store the gradient with respect to ``x``.

# In[2]:


x.attach_grad()


# Record the computation within the `record` scope.

# In[3]:


with autograd.record():
    y = 2.0 * np.dot(x, x)
y


# The gradient of the function $y = 2\mathbf{x}^{\top}\mathbf{x}$ with respect to $\mathbf{x}$ should be $4\mathbf{x}$. 

# In[4]:


y.backward()
x.grad - 4 * x