The derivative of a function can be found by letting go to in the difference quotient:
Normally you do not find the derivative this way, but by using differentiation rules of which you already know some.
Differentiation rule 1 (power rule):
If then for any and for integer positive .
Differentiation rule 2 (rule for constants):
If then .
Differentiation rule 3 (sum rule):
If then .
These differentiation rules are useful when computing the slope of the graph of a function that consists of the sum (or difference) of power functions with positive integer exponents. When dealing with other functions, other differentiation rules are needed.