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AP Calculus BC/Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
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Chain Rule with Arctangent and Exponentials

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If $y = \arctan(e^x) + \arctan(e^{-x})$, then $\frac{dy}{dx} =$

A

ex1+(ex)2+e−x1+(e−x)2\frac{e^x}{1+(e^x)^2} + \frac{e^{-x}}{1+(e^{-x})^2}

B

00

C

ex1+(ex)2−e−x1+(e−x)2\frac{e^x}{1+(e^x)^2} - \frac{e^{-x}}{1+(e^{-x})^2}

D

ex−e−x(1+(ex)2)(1+(e−x)2)\frac{e^x-e^{-x}}{(1+(e^x)^2)(1+(e^{-x})^2)}

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