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Power function

The power function is

a g^h

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

 

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Explanation

You can also write it as

f (x) = a g (x)^h (x)

 

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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.

 

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Example 2

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

 

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