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: 25

Answer

Rewrite: $\frac{5x^{-2}}{2}$; Differentiate: $\frac{(5)(-2)(x^{-3})}{2}$; Simplify: $\frac{-5}{x^{3}}$

Work Step by Step

To rewrite, you use the index rule which states that $\frac{1}{x^n}$ is equal to $x^{-n}$ which gives you $\frac{5x^{-2}}{2}$. To differentiate, use the power rule to find the derivative of $x^{-2}$ which is $-2x^{-2-1}$ hence the derivative of the function is $\frac{(5)(-2)x^{-3}}{2}$. Finally to simplify, you can cancel the $2$ from up and down and take the variable to the denominator (as a general rule of thumb, you should give the answer in simplest form or in the same form you were given) hence the final simplified answer is $\frac{-5}{x^{3}}$.
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