Find the Derivative - d/dx 4e^x

Problem

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

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

2. Apply the rule by moving the constant 4 outside of the derivative operator.

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

3. Differentiate the exponential function e^x noting that the derivative of e^x with respect to x is simply e^x

d(e^x)/d(x)=e^x

4. Multiply the constant back into the result to find the final derivative.

4⋅e^x=4*e^x

Final Answer

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

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