University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Questions to Guide Your Review - Page 201: 27


See below.

Work Step by Step

We can rewrite any real power of x as a power of $e$, like so: $x^n= e^{n\ln x}$ with the restriction $x\gt0$ On taking the derivative, we get: $\frac{d(x^n)}{dx}=\frac{d(e^{n\ln x})}{dx}$ Applying the chain rule, gives us: $\frac{d(x^n)}{dx}=(e^{n\ln x})\frac{d({n\ln x})}{dx}$ $\frac{d(x^n)}{dx}=(e^{n\ln x})\frac{({n})}{x}$ $\frac{d(x^n)}{dx}=(x^n)\frac{({n})}{x}$ $\frac{d(x^n)}{dx}=nx^{(n-1)}$ Which is the power rule for derivatives.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.