Power Rule
Power means exponent, such as the 2 in x^{2}
The Power Rule, one of the most commonly used derivative rules, says:
The derivative of x^{n} is nx^{(n−1)}
Example: What is the derivative of x^{2} ?
For x^{2} we use the Power Rule with n=2:
The derivative of x^{2}  =  2x^{(2−1)} 
=  2x^{1} 

=  2x 
Answer: the derivative of x^{2} is 2x
"The derivative of" can be shown with this little "dash" mark: ’
Using that mark we can write the Power Rule like this:
f’(x^{n}) = nx^{(n−1)}
Example: What is the derivative of x^{3} ?
f’(x^{3}) = 3x^{3−1} = 3x^{2}
"The derivative of" can also be shown by \frac{d}{dx}
Example: What is \frac{d}{dx}(1/x) ?
1/x is also x^{−1}
Using the Power Rule with n = −1:
\frac{d}{dx}x^{n} = nx^{n−1}
\frac{d}{dx}x^{−1} = −1x^{−1−1} = −x^{−2}
How to Remember
"multiply by power
then reduce power by 1"
A Short Table
Here is the Power Rule with some sample values. See the pattern?
f  f’(x^{n}) = nx^{(n−1)}  f’ 

x  1x^{(1−1)} = x^{0}  1 
x^{2}  2x^{(2−1)} = 2x^{1}  2x 
x^{3}  3x^{(3−1)} = 3x^{2}  3x^{2} 
x^{4}  4x^{(4−1)} = 4x^{3}  4x^{3} 
etc...  
And for negative exponents:  
x^{−1}  −1x^{(−1−1)} = −x^{−2}  −x^{−2} 
x^{−2}  −2x^{(−2−1)} = −2x^{−3}  −2x^{−3} 
x^{−3}  −3x^{(−3−1)} = −3x^{−4}  −3x^{−4} 
etc... 
6800, 6801, 6802, 6803, 6804, 6805, 13384, 13385, 13386, 13387