Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.3 Introduction To Techniques Of Differentiation - Exercises Set 2.3: 21

Answer

$\left[ \frac{dy}{dx}\right]_{x=1} = 15 $

Work Step by Step

Let $ y = 1 + x + x^2 + x^3 + x^4 + x^5 $. $$ \frac{dy}{dx} = 0 + 1 + 2x + 3x^2 + 4x^3 + 5x^4 $$ Now, let us evaluate the value of the derivative at $x = 1$: $$ \begin{align} \frac{dy}{dx}|_{x=1} &= 0 + 1 + 2\cdot 1 + 3 \cdot 1^2 + 4\cdot1^3 + 5\cdot1^4 \\ &= 1 + 2 + 3 + 4 + 5 \\ &= 15 \end{align} $$
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