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: 26


Rewrite: $\frac{3}{2}x^{-4}$; Differentiate: $(\frac{3}{2})(-4)(x^{-4-1})$; Simplify: $\frac{-6}{x^5}$ .

Work Step by Step

To rewrite, use the index rule $\frac{1}{x^n}$ is equal to $x^{-n}$; hence, the function becomes $(\frac{3}{2})(x^{-4})$. To differentiate, use the power rule to find the derivative of $x^{-4}$ which is $(-4)(x^{-4-1})$; hence, the derivative of the overall function is just the derivative of $x^{-4}$ times the constant $\frac{3}{2}$. To simplify, both the numerator and denominator can be simplified by two leaving a $-6$; furthermore, $x^{-5}$ can be taken to the denominator; hence, the overall simplified derivative is $\frac{-6}{x^5}$.
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