CK12 Calculus - Single Variable

Proof:

Example1:
Iff(x) = 16 for allx, thenf(x) = 0 for all x. We can also writed/dx (16) = 0.

The PowerRuleIfnis a positiveinteger, then for all real valuesofx

The proofis omittedin this text,but it is availableat

http://en.wikipedia.org/wiki/Calculus_with_polynomials.

Example2:

Iff(x) =x^3 , then

f(x) = 3x3-1= 3x^2

and

The PowerRuleand a Constant

If is a constantand is differentiableat all , then

In simplernotation,

In otherwords,the derivativeof a constanttimesa function

is equalto the constanttimesthe derivativeof the function.

Example3: