Find the Derivative - d/d@VAR f(x)=e^(-2x)

Problem

d()/d(x)*e(−2*x)

Solution

1. Identify the function as a composition of the exponential function eu and the linear function u=−2*x

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

3. Differentiate the inner function u=−2*x with respect to x to get d(u)/d(x)=−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(−2*x))/d(x)=−2*e(−2*x)

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