`G(y) = ln(((2y+1)^5)/(sqrt(y^2 + 1)))` Differentiate the function.

Textbook Question

Chapter 3, 3.6 - Problem 13 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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mathace | (Level 3) Assistant Educator

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Given: `G(y)=ln((2y+1)^5/sqrt(y^2+1))`

Rewrite the equation using the Law of Logarithms. Then find the derivative of the function. 

`G(y)=5ln(2y+1)-(1)/(2)ln(y^2+1)`

`G'(y)=(5)/(2y+1)(2)-(1)/(2(y^2+1))(2y)`

The derivative is: `G'(y)=(10)/(2y+1)-(y)/(y^2+1)`

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