Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Practice Exercises - Page 177: 24



Work Step by Step

Rewrite the equation: $y=x^{1/2}csc(x+1)^3$ Take the derivative of the equation using Power Rule, Product Rule, Trigonometric derivatives, and Chain Rule: $y'=x^{1/2}\times-csc(x+1)^3cot(x+1)^3\times3(x+1)^2\times1+\frac{1}{2}x^{-1/2}csc(x+1)^3$ $=-3x^{1/2}(x+1)^2csc(x+1)^3cot(x+1)^3+\frac{1}{2}x^{-1/2}csc(x+1)^3$
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