Let p ∈ Q. Define f (x) = xp for x > 0. Prove that f is differentiable on (0, ∞) and thatf ′(x) = pxp−1 for all x > 0

Question

Let p ∈ Q. Define f (x) = xp for x > 0. Prove that f is differentiable on (0, ∞) and thatf ′(x) = pxp−1 for all x > 0
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Solution 1

To prove that the function f(x) = xp is differentiable on (0, ∞) and that f'(x) = pxp-1 for all x > 0, we can use the power rule for differentiation, which states that the derivative of x^n, where n is any real number, is nx^(n-1).

Step 1: Define the function Let's define the function f(x) = xp, wh Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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