Find the Derivative - d/dx 8e^x

Problem

(d(8)*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 that function.

2. Apply the constant multiple rule by moving the constant 8 outside of the derivative operator.

(d(8)*ex)/d(x)=8d(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 simply ex

d(ex)/d(x)=ex

4. Multiply the constant 8 by the result of the derivative to find the final expression.

8⋅ex=8*ex

Final Answer

(d(8)*ex)/d(x)=8*ex

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