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Derivative of a higher degree
The derivative of a higher degree is
Explanation
We take the function
Substitution in the definition of the derivative gives
Use the formula of the long division
with a = x + Δx and b = x for then you get a – b = Δx. Substitution gives
The limit of a sum is the sum of the limits, so that
There are n terms, so
The formula applies for every whole, broken and negative exponent.