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# Power rule with irrationals?

Is derivative of X^irrational = nx^(n-1) where n is irrational. Proving power rule by binomial expansion we restrict the domain of n to integers as the proof of binomial expansion is proved by Mac Lauren series which uses the fact of power rule. Can somebody show me proof of power rule when n is irrational? Example x^(root2)?

Note by Ritik Agrawal
4 months, 2 weeks ago

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Use logarithmic differentiation:

y= x^A

ln y = A * ln x

1/y * dy/dx = A/x

dy/dx = A * y/x = A * x^(A-1)

- 4 months, 1 week ago