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: 50

Answer

The derivative is $\frac{2}{3\sqrt[3] t}-\frac{1}{3\sqrt[3] {t^2}}$.

Work Step by Step

To find the derivative of the overall function just apply the power rule$((x^n)'=nx^{n-1})$ to the individual terms as follows: $f'(t)=(t^{\frac{2}{3}}-t^{\frac{1}{3}}+4)'$ $=(t^{\frac{2}{3}})'-(t^{\frac{1}{3}})'+(4)'$ $=\frac{2}{3}t^{\frac{2}{3}-1}-\frac{1}{3}t^{\frac{1}{3}-1}+0=$ $\frac{2}{3\sqrt[3] t}-\frac{1}{3\sqrt[3] {t^2}}.$
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