List Comprehension and Patterns in Higher Derivatives in Python
Author: David Manuel
In this video, it is shown how to use Python to quickly find several derivatives of a function using Python's list comprehension tool. We can then find the patterns in the results allowing us to write a formula for all higher order derivatives of the function.
Transcript 14
Transcript 14
Exercises
Python Code:
from sympy import *
# List Comprehension
x=symbols('x')
f=1/x
# 1st 6 derivatives IN ONE LINE OF CODE!
fderivs=[diff(f,x,i) for i in range(1,7)]
#range(a,b)-> list of integers from a INCLUSIVE to b EXCLUSIVE
print(fderivs)
# exponent is 1 bigger than the derivative we took: x^(n+1)
# signs alternate (-1)^n or (-1)^(n+1). n=1 is negative, so (-1)^n
#factorial numbers in the numerator: n!
print('The formula for the nth derivative of f is (-1)^n*n!/x^(n+1)')
Open Python Notebook File
from sympy import *
# List Comprehension
x=symbols('x')
f=1/x
# 1st 6 derivatives IN ONE LINE OF CODE!
fderivs=[diff(f,x,i) for i in range(1,7)]
#range(a,b)-> list of integers from a INCLUSIVE to b EXCLUSIVE
print(fderivs)
# exponent is 1 bigger than the derivative we took: x^(n+1)
# signs alternate (-1)^n or (-1)^(n+1). n=1 is negative, so (-1)^n
#factorial numbers in the numerator: n!
print('The formula for the nth derivative of f is (-1)^n*n!/x^(n+1)')
Open Python Notebook File
Related Videos (200)
Antiderivatives: MATH 171 Problems 4-6
Proving facts about antiderivatives and a physics application
MLC WIR 20B M151 week6 #5c
Using the Chain Rule to find the derivative of a composition of functions
