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

# This worksheet is based on SageMath 7.4.beta2 + [branch of ticket #21286](https://trac.sagemath.org/ticket/21286)

# In[1]:


version()


# In[2]:


get_ipython().run_line_magic('display', 'latex')


# In[3]:


var('x y')
F = function('f')(x,y)
F


# In[4]:


diff(F,x)


# In[5]:


print(diff(F,x))


# In[6]:


diff(F,x,y)


# In[7]:


print(diff(F,x,y))


# In[8]:


diff(F,y,x)


# In[9]:


diff(F,x,x,x)


# In[10]:


diff(F,x,y,x)


# In[11]:


diff(F,x,x,y)


# In[12]:


diff(F,x,y,y)


# In[13]:


G = function('g')(x)
G


# In[14]:


diff(G,x)


# In[15]:


var('th', latex_name=r'\theta')


# In[16]:


H = function('h')(th)
H


# In[17]:


diff(H,th)


# In[18]:


print(diff(H,(th)))


# In[19]:


diff(F,th)


# In[20]:


diff(f(th,y),y)


# In[21]:


diff(f(g(th),y),y)


# In[22]:


diff(f(g(th),y),th)


# In[23]:


print(diff(f(g(th),y),th))


# In[24]:


F.diff(x)


# In[25]:


F.differentiate(x,y)


# In[26]:


diff(F,x)(0,1)


# In[27]:


diff(F,x)(x=0,y=y)


# In[28]:


diff(F,x)(y,x)


# In[29]:


diff(F,x)(x=y,y=y)


# In[30]:


diff(F,x)(x=y,y=x)


# In[31]:


diff(f(x+y,y),x)


# In[32]:


print(diff(f(x+y,y),x))


# In[33]:


diff(f(x+y,y),y)


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