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

Problem

d(e(2*x))/d(x)

Solution

1. Identify the function as a composition of the natural 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 which results in (d(2)*x)/d(x)=2

4. Multiply the derivative of the outer function by the derivative of the inner function to get e(2*x)⋅2

5. Simplify the expression by placing the constant coefficient in front.

Final Answer

d(e(2*x))/d(x)=2*e(2*x)

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