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: 39


The derivative is $2x+6x^{-3}$.

Work Step by Step

To find the overall derivative, we find the derivatives of the individual terms being added/subtracted and we add them. We use the power rule $((x^n)' = nx^{n-1})$ to differentiate the terms. The derivative of $x^2$ is $2x$. The derivative of $5$ is $0$. The derivative of $-3x^{-2}$ is $(-3)(-2)(x^{-2-1})$ which simplifies to $6x^{-3}$. N.B. while an answer is always expected to be simplified completely, you are allowed to give it in the same format given to you. Since in the given question the exponent was negative, you may leave it as negative or take the expression to the denominator to change the exponent to positive.
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