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Differentiate the following w.r.t. x: si...

Differentiate the following w.r.t. x:
`sin(tan^(-1)e^(-x))`

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AI Generated Solution

To differentiate the function \( y = \sin(\tan^{-1}(e^{-x})) \) with respect to \( x \), we will use the chain rule. Here are the steps: ### Step 1: Differentiate the outer function We start by differentiating the outer function, which is \( \sin(u) \), where \( u = \tan^{-1}(e^{-x}) \). Using the derivative of sine: \[ \frac{dy}{dx} = \cos(u) \cdot \frac{du}{dx} ...
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