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: 46

Answer

The derivative is $8x-\frac{5}{x^2}$.

Work Step by Step

First, split the numerator to get $h(x)=\frac{4x^3}{x}+\frac{2x}{x}+\frac{5}{x}=4x^2+2+\frac{5}{x}$. Then, rewrite $h(x)$ as $h(x)=4x^2+2+5x^{-1}$. To differentiate $h(x)$, differentiate the individual terms using the power rule and sum up the results. The derivative of $4x^2$ is $8x$. The derivative of $2$ is $0$. The derivative of $5x^{-1}$ is $(5)(-1)(x^{-1-1})$which simplifies to $-\frac{5}{x^2}$. Summing everything together gives us $h'(x)=x-\frac{5}{x^2}$.
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