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: 30


Rewrite: $4x^3$; Differentiate: $(4)(3)(x^{3-1})$; Simplify: $12x^2$.

Work Step by Step

To simplify, just use the same index rule to take $x^{-3}$ to the numerator; hence, the function becomes $4x^3$. To differentiate just use the power rule to find the derivative of $x^3$ which is $3x^{3-1}$ so the overall derivative is $(4)(3)(x^{3-1})$. To simplify, just multiply the constants together to get $12x^2$.
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