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Power function

The power function is

a gh

in which g and h can both be a function of x.



You can also write it as

f (x) = a g (x)h (x)


Example 1

In a power function with a negative number as base, this number must be put in brackets. In the calculation

(−2)4 = 16

the brackets indicate that you work with powers of the negative number −2. For odd powers you get

(−2)3 = −8 = −23

In the calculation

−24 = − (+2)4 = −16

you work with powers of the positive number +2.


Example 2

The derivative of the power function f (x) = xx has the solution


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