Find the Derivative - d/dx 2e^(3x)

Problem

(d(2)*e(3*x))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

(d(2)*e(3*x))/d(x)=2d(e(3*x))/d(x)

2. Apply the chain rule for the exponential function eu where u=3*x

d(eu)/d(x)=eu⋅d(u)/d(x)

3. Differentiate the exponent 3*x with respect to x

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

4. Multiply the results together to find the final derivative.

2⋅e(3*x)⋅3=6*e(3*x)

Final Answer

(d(2)*e(3*x))/d(x)=6*e(3*x)

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