The Power Rule in Calculus is used when finding derivatives, and can be simplified to the following steps:
The result of taking the derivative of f(x) is often written as f'(x) (f prime of x).
To generalise:
d/dx x^{n} = nx^{n1}
Some examples:
f 
d/dx 
f' 
Notes 
f(x^{3}) 
x^{3} = (3)x^{31} = 3x^{2} 
3x^{2} 

f(x^{2}) 
x^{2} = (2)x^{21} = 2x^{1} = 2x 
2x 

f(x) 
x = x^{1} = (1)x^{11} = x^{0} = 1 
1 
x is the same as x^{1} Any term raised to the power of 0 is always 1 
f(x^{0}) 
x^{0} = (0)x^{01} = 0^{1} = 0 
0 

f(x^{1}) 
x^{1} = (1)x^{11} = x^{2} 
x^{2}or: 1/x^{2} 
This can be written either way 
f(x^{2}) 
x^{2} = (2)x^{21} = 2x^{3} 
2x^{3}or: 2/x^{3} 
This can be written either way 
f(x^{3}) 
x^{3} = (3)x^{31} or: = 3x^{4} 
3x^{4}or: 3/x^{4} 
This can be written either way 
Copyright © 2018 ELIASdigital.com