Find the Derivative - d/dx f(x)=e^(3x)

Problem

d(e(3*x))/d(x)

Solution

1. Identify the function as an exponential function of the form eu where u is a function of x

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

3. Determine the derivative of the exponent u=3*x which is (d(3)*x)/d(x)=3

4. Multiply the original exponential function by the derivative of the exponent to find the final result.

Final Answer

d(e(3*x))/d(x)=3*e(3*x)

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