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Find the derivative of $f(x)$ . Where $f(x)=e^{(x+1)}$ $f'(x) = ?$

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Find derivatives using the chain rule I

Full solution

Q. Find the derivative of

f(x)

. Where

f(x)=e^{(x+1)}

f'(x) = ?

Identify function: Identify the function to differentiate. $f(x) = e^{(x+1)}$ .
Apply derivative rule: Apply the derivative rule for exponential functions. The derivative of $e^u$ , where $u$ is a function of $x$ , is $e^u$ times the derivative of $u$ .
Find inner function derivative: Find the derivative of the inner function $u(x) = x+1$ . The derivative of $u(x)$ is $1$ .
Multiply derivative and function: Multiply the derivative of the inner function by the original function. $f'(x) = e^{(x+1)} \times 1$ .
Simplify expression: Simplify the derivative expression. $f'(x) = e^{(x+1)}$ .

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