Problem

Find the derivative of the function.
\[
f(x)=e^{2-x}
\]
\[
f^{\prime}(x)=
\]
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Answer

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Answer

So, the final answer is \(\boxed{-e^{2-x}}\).

Steps

Step 1 :The function given is \(f(x)=e^{2-x}\).

Step 2 :We need to find the derivative of this function.

Step 3 :The derivative of a function can be found 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.

Step 4 :In this case, the outer function is \(e^u\) and the inner function is \(2-x\).

Step 5 :The derivative of \(e^u\) is \(e^u\) and the derivative of \(2-x\) is -1.

Step 6 :Therefore, the derivative of the function \(f(x) = e^{2-x}\) is \(-e^{2-x}\).

Step 7 :So, the final answer is \(\boxed{-e^{2-x}}\).

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