# Numerical Differentiation in Python

Learn how to differentiate a sequence or list of values numerically

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In [1]:

```
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 FunctionÂ¶

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

In [2]:

```
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')
```

Out[2]: