Find the Derivative - d/dx e^(-x/2)

Problem

d(e(−x/2))/d(x)

Solution

1. Identify the outer function as the exponential function eu and the inner function as u=−x/2

2. Apply the chain rule, which states that d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the inner function u=−1/2*x with respect to x to get −1/2

4. Multiply the derivative of the outer function by the derivative of the inner function.

5. Simplify the resulting expression.

Final Answer

d(e(−x/2))/d(x)=−1/2*e(−x/2)

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