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: 45

Answer

$f'(x)=1-\frac{8}{x^3}$ .

Work Step by Step

First, split the numerator: $f(x) = \frac{x^3}{x^2}-\frac{3x^2}{x^2}+\frac{4}{x^2}=x-3+\frac{4}{x^2}$. Rewrite the function as $f(x) = x-3+4x^{-2}$. To differentiate, use the power rule $((x^n)'=nx^{n-1})$ on the individual terms: The derivative of $x$ is $1$. The derivative of $-3$ is $0$. The derivative of $4x^{-2}$ is equal to $(4)(-2)(x^{-2-1})$ which simplifies to $-\frac{8}{x^3}$. Summing everything together gives $f'(x)=1-\frac{8}{x^3}$.
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