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

Problem

d()/d(x)*5*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 the function.

2. Apply the constant multiple rule by moving the 5 outside of the derivative operator.

(d(5)*ex)/d(x)=5d(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 back into the result to find the final derivative.

5⋅ex=5*ex

Final Answer

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

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