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

Problem

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

Solution

1. Identify the function as a composite function of the form eu where u=3*x

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

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

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

5. Simplify the resulting expression.

Final Answer

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

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