`y = e^(k tan(sqrt(x)))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 38 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro | College Teacher | (Level 1) Educator Emeritus

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`y'= d/dx e^(ktan(sqrt(x)))`

`= e^(ktan(sqrt(x))) d/dx (ktan(sqrt(x)))`

`= k e^(ktan (sqrt(x))) * sec^2(sqrt(x)) * d/dx (sqrt(x))`

`= k*e^(ktan(sqrt(x))) * sec^2(sqrt(x))*(1/2 x^(-1/2))`

`= k/(2sqrt(x)) *e^(ktan(sqrt(x))) * sec^2(sqrt(x))`

Hope this helps.

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