Find the Derivative - d/dx e^(1-x)

Problem

d(e^(1−x))/d(x)

Solution

1. Identify the rule needed for the differentiation, which is the chain rule for exponential functions of the form e^u

2. Apply the formula for the derivative of e^u which states that d(e^u)/d(x)=e^u⋅d(u)/d(x)

3. Define the inner function u=1−x

4. Differentiate the inner function to find d(u)/d(x)=−1

5. Substitute the components back into the chain rule formula to get e^(1−x)⋅(−1)

6. Simplify the expression by moving the negative sign to the front.

Final Answer

d(e^(1−x))/d(x)=−e^(1−x)

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