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 eu

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