Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 146: 30



Work Step by Step

The chain rule states that if y=g(h(x)), then y'=g'(h(x))h'(x). Since y=$sin^{2}$(x), which we'll begin by rewriting as $(sin(x))^{2}$, we can set g(x)=$x^{2}$ (outside function) and h(x)=sin(x) (inside function), and use the chain rule to find y'. Therefore, y'=g'(sin(x))h'(x) We know that $\frac{d}{dx}$[$x^{2}$]=2x, using the power rule $\frac{d}{dx}$[sin(x)]=cos(x), it'd be a good idea to memorize this derivative Now that we know that g'(x)=2x and h'(x)=cos(x), we can find y'. y'=2(sin(x))*(cos(x)) =2sin(x)cos(x)
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