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The Power Rule - Calculus - 04 Jun 2018 at 02:06

Articles about The Power Rule - Calculus

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The Power Rule - Calculus

The Power Rule in Calculus is used when finding derivatives, and can be simplified to the following steps:

  1. Multiply the term by the exponent (power)
  2. Subtract 1 from the exponent

The result of taking the derivative of f(x) is often written as f'(x) (f prime of x).

To generalise:

d/dx xn = nxn-1

Some examples:

f
d/dx
f'
Notes
f(x3)
x3
= (3)x3-1
= 3x2
3x2
 
f(x2)
x2
= (2)x2-1
= 2x1
= 2x
2x
 
f(x)
x
= x1
= (1)x1-1
= x0
= 1
1

x is the same as x1

Any term raised to the power of 0 is always 1

f(x0)
x0
= (0)x0-1
= 0-1
= 0
0
 
f(x-1)
x-1
= (-1)x-1-1
= -x-2
-x-2
or:
-1/x2
This can be written either way
f(x-2)
x-2
= (-2)x-2-1
= -2x-3
-2x-3
or:
-2/x3
This can be written either way
f(x-3)
x-3
= (-3)x-3-1
or:
= -3x-4
-3x-4
or:
-3/x4
This can be written either way

 

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