Numerical differentiation

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Differentiate the Sine Function

How to use numerical differentiation to plot the derivative of the sine function $y = sin(x)$:

x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)

dy = np.zeros(y.shape,np.float)
dy[0:-1] = np.diff(y)/np.diff(x)
dy[-1] = (y[-1] - y[-2])/(x[-1] - x[-2])

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='sin(x)'
)

trace2 = go.Scatter(
    x=x,
    y=dy,
    mode='lines',
    name='numerical derivative of sin(x)'
)

trace_data = [trace1, trace2]
py.iplot(trace_data, filename='numerical-differentiation')

from IPython.display import display, HTML

display(HTML('<link href="//fonts.googleapis.com/css?family=Open+Sans:600,400,300,200|Inconsolata|Ubuntu+Mono:400,700" rel="stylesheet" type="text/css" />'))
display(HTML('<link rel="stylesheet" type="text/css" href="http://help.plot.ly/documentation/all_static/css/ipython-notebook-custom.css">'))

! pip install git+https://github.com/plotly/publisher.git --upgrade
import publisher
publisher.publish(
    'python_Numerical_Differentiation.ipynb', 'python/numerical-differentiation/', 'Numerical Differentiation | plotly',
    'Learn how to differentiate a sequence or list of values numerically',
    title='Numerical Differentiation in Python. | plotly',
    name='Numerical Differentiation',
    language='python',
    page_type='example_index', has_thumbnail='false', display_as='mathematics', order=6,
    ipynb= '~notebook_demo/102')
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