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What is the derivative of xn, where n is some natural number (1, 2, 3, ...)?

Thanks.

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2 Answers

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nxn-1

In words:


multiply by the power, and
lower the power by 1


Also, it should be noted that this works for any type of number, n, not just the natural numbers (even works for complex numbers, for the Specialist Maths students)

Tip: This can be used for a lot more functions than it might seem at first:


Look out for roots and reciprocals and convert them into powers (i.e.: sqrt(x) = x1/2 and 1/x = x-1)
This makes this rule extremely flexible for a heap of situations!


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if n is a positive integer, then:

dy/dx = n*x^(n-1)

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