Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 122: 31



Work Step by Step

The product rule when there are 3 operands is $(uvw)'=u'vw+uv'w+uvw'$ Therefore, $f'(x)=\frac{d}{dx}(x+3)\times(x-1)(x-5)+(x+3)\times\frac{d}{dx}(x-1)\times(x-5)+(x+3)(x-1)\frac{d}{dx}(x-5)$ $=1\times(x-1)(x-5)+(x+3)\times1\times(x-5)+(x+3)(x-1)\times1$ $=x^{2}-5x-x+5+x^{2}-5x+3x-15+x^{2}-x+3x-3$ $=3x^{2}-6x-13$
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