Find the Derivative - d/d@VAR f(x)=5e^x

Problem

d()/d(x)*5*e^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 5 outside of the derivative operator.

(d(5)*e^x)/d(x)=5d(e^x)/d(x)

3. Recall the derivative rule for the natural exponential function, which states 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.

5⋅e^x=5*e^x

Final Answer

(d(5)*e^x)/d(x)=5*e^x

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