`f(t) = sin^2(e^(sin^2(t)))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 41 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

`y' = d/dt [sin^2(e^(sin^2t))]`

`= 2 sin(e^(sin^2t))*d/dt(sin(e^(sin^2t)))`

`= 2 sin(e^(sin^2t))* cos(e^(sin^2t))*d/dt (e^(sin^2t)))`

`= 2 sin(e^(sin^2t))*cos(e^(sin^2t))*e^(sin^2t)*2sint*cost`

`= 4 sint * cost * e^(sin^2t)* sin(e^(sin^2t))* cos(e^(sin^2t))`

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balajia's profile pic

balajia | College Teacher | (Level 1) eNoter

Posted on

`f(t)=sin^2(e^(sin^2t))`

`f'(t)=2sin(e^(sin^2t)).cos(e^(sin^2t)).e^(sin^2t)(2sint.cost)`

`f'(t)=sin(2e^(sin^2t)).sin(2t).e^(sin^2t)`

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