Differentiation rules > Differentiation rules
123456Differentiation rules

Theory

The derivative of a function y = f ( x ) can be found by letting h go to 0 in the difference quotient:
f ( x + h ) - f ( x ) h

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 f ( x ) = c x n then f ( x ) = n c x n 1 for any c and for integer positive n .

Differentiation rule 2 (rule for constants):
If f ( x ) = c then f ( x ) = 0 .

Differentiation rule 3 (sum rule):
If f ( x ) = u ( x ) ± v ( x ) then f ( x ) = u ( x ) ± v ( x ) .

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.

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