Calculate the derivative of the following function. \[ y=\tan \left(e^{x}\right) \] \[ \frac{d y}{d x}= \]

Step 1 ：The derivative of a function can be calculated using the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is \(\tan(x)\) and the inner function is \(e^x\). The derivative of \(\tan(x)\) is \(\sec^2(x)\) and the derivative of \(e^x\) is \(e^x\). Therefore, the derivative of the function \(y = \tan(e^x)\) is \(\frac{dy}{dx} = \sec^2(e^x) * e^x\).

Step 2 ：The derivative of the function \(y = \tan(e^x)\) is \(\frac{dy}{dx} = (\tan(\exp(x))^2 + 1)*\exp(x)\). This is the final answer.

Step 3 ：Final Answer: \(\frac{d y}{d x}=\boxed{\left(\tan\left(e^{x}\right)^{2}+1\right) e^{x}}\)