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

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Find the derivative of  f(x).  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, the derivative of e^(x+1) with respect to x+1 is e^(x+1).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.Multiply Derivatives: Multiply the derivatives from Step 3 and Step 4. According to the chain rule, we multiply the derivative of the outer function by the derivative of the inner function. This gives us the derivative of f(x) with respect to x: f'(x) = e^(x+1) * 1.Simplify Expression: Simplify the expression. Multiplying e^(x+1) by 1 does not change the expression, so the derivative f'(x) remains e^(x+1).

Find the derivative of $\newline$ $f(x)$ . $\newline$ $f(x)=e^{(x+1)}$

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Find the derivative of \newlinef(x)f(x)f(x).\newlinef(x)=e(x+1)f(x)=e^{(x+1)}f(x)=e(x+1)

Find the derivative of $\newline$ $f(x)$ . $\newline$ $f(x)=e^{(x+1)}$