Find the Derivative - d/dx 5e^x

Problem

(d(5)*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 constant multiple rule by moving the constant 5 outside of the derivative.

(d(5)*ex)/d(x)=5d(ex)/d(x)

3. Recall the derivative of the natural exponential function ex which is simply ex

d(ex)/d(x)=ex

4. Multiply the constant 5 by the result of the derivative.

5⋅ex=5*ex

Final Answer

(d(5)*ex)/d(x)=5*ex

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