Find the Derivative - d/dx 4e^x

Problem

(d(4)*ex)/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)*ex)/d(x)=4d(ex)/d(x)

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

d(ex)/d(x)=ex

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

4⋅ex=4*ex

Final Answer

(d(4)*ex)/d(x)=4*ex

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