Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 28

Answer

Rewrite: $(\frac{\pi}{9})(x^{-2})$; Differentiate: $(\frac{\pi}{9})(-2)(x^{-2-1})$; Simplify: $\frac{-2\pi}{9x^3}$.

Work Step by Step

First, remember that $\pi$ is a CONSTANT hence we treat it like any number! To rewrite, notice that not only is $x$ raised to the power of two but $3x$ is; hence the denominator becomes $9x^2$. Then, using the index rule($\frac{1}{x^n}=x^{-n}$) take $x^2$ to the numerator to get $(\frac{\pi}{9})(x^{-2})$. To differentiate, use the power rule to get the derivative of $x^{-2}$ which is $(-2)(x^{-2-1})$; hence the overall derivative is the derivative of $x^{-2}$ times $\frac{\pi}{9}$ which is $(\frac{\pi}{9})(-2)(x^{-2-1})$. To simplify, all you have to do is take $x^{-3}$ to the denominator to get overall $\frac{-2\pi}{9x^3}$.
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