`y = sqrt(1 + 2e^(3x))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 23 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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nick-teal | High School Teacher | (Level 3) Adjunct Educator

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`y' = 1/(2sqrt(1 + 2e^(3x))) * (d/(dx))(1 + 2e^(3x))`

`y' = 1/(2sqrt(1 + 2e^(3x))) (3*2e^(3x))`

`y' = 3e^(3x)/sqrt(1 +2e^(3x))`

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gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

`y' = d/dx(1+2e^3x)^(1/2) = (1/2)*(1+2e^3x)^(1-1/2)*d/dx(1+2e^3x)`

`= (1/2)(1+2e^3x)^(-1/2)*(2e^3)`

`=e^3/sqrt[1+2e^3x]`

hope this helps.

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