Find the Derivative - d/d@VAR F(X)=4e^X

Problem

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

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 that function.

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

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

3. Recall the derivative rule for the natural exponential function, which states that the derivative of ex with respect to x is ex

d(ex)/d(x)=ex

4. Multiply the constant 4 by the result of the derivative.

4⋅ex=4*ex

Final Answer

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

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