Prove (Theorem 2.3) that

for the case in which n is a rational number. Write y = x^p/q in the form y^q = x^p and differentiate implicitly. Assume that p and q are integers, where q > 0.)

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THEOREM 2.3 The Power Rule If n is a rational number, then the function f(x) =x" is differentiable and [x]=nxn-! d dx For f to be differentiable at x = 0, n must be a number such that xn-¹ is defined on an interval containing 0.