Find the Derivative - d/dx 4e^(2x)

Problem

(d(4)*e(2*x))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 4 to be moved outside the derivative.

(d(4)*e(2*x))/d(x)=4d(e(2*x))/d(x)

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

d(e(2*x))/d(x)=e(2*x)⋅(d(2)*x)/d(x)

3. Differentiate the inner function 2*x with respect to x

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

4. Substitute the result back into the expression and multiply the constants.

4⋅e(2*x)⋅2=8*e(2*x)

Final Answer

(d(4)*e(2*x))/d(x)=8*e(2*x)

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