Find the derivative of the function. \[ f(x)=\arctan \left(e^{x}\right) \] \( f^{\prime}(x)=\square \)

To find the derivative of the function \( f(x) = \arctan(e^{x}) \), we can use the chain rule. The derivative of \( \arctan(u) \) with respect to \( u \) is \( \frac{1}{1+u^2} \), where \( u = e^{x} \). Therefore, applying the chain rule, we get: \[ f'(x) = \frac{1}{1 + (e^{x})^2} \cdot e^{x} \] Thus, the derivative is: \[ f'(x) = \frac{e^{x}}{1 + e^{2x}} \]