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: 52

Answer

The derivative is $\frac{-2}{3x\sqrt[3] x}-3sin(x)$.

Work Step by Step

To find $f'(x)$ just apply the power rule $((x^n)'=nx^{n-1})$ to the terms that make up the function as follows after rewriting as $f(x)=2x^{-\frac{1}{3}}+3cos(x)$ $f'(x)=(2x^{-\frac{1}{3}}+3cos(x))'=(2x^{-\frac{1}{3}})'+(3cos(x))'=$ $(2)(-\frac{1}{3})(x^{-\frac{1}{3}-1})+(3)(-sin(x))=\frac{-2}{3x\sqrt[3] x}-3sin(x)$
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