Find the derivative f(x)=e^(x+1)

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Identify function: Identify the function to differentiate. We are given the function f(x) = e^(x+1) and we need to find its derivative with respect to x.Apply chain rule: Apply the chain rule for differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is e^u (where u = x+1) and the inner function is u = x+1.Differentiate outer function: Differentiate the outer function with respect to the inner function. The derivative of e^u with respect to u is e^u. So, we have d/du(e^u) = e^u.Differentiate inner function: Differentiate the inner function with respect to x. The derivative of u = x+1 with respect to x is 1, since the derivative of x is 1 and the derivative of a constant is 0. So, we have du/dx = 1.Apply chain rule: Apply the chain rule using the results from steps 3 and 4. The derivative of f(x) with respect to x is the product of the derivatives from steps 3 and 4. Therefore, f'(x) = e^(x+1) * 1.Simplify derivative: Simplify the expression for the derivative. Since multiplying by 1 does not change the value, the derivative simplifies to f'(x) = e^(x+1).

Find the derivative $f(x)=e^{(x+1)}$

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