Find the Derivative - d/dx (e^x)/x

Problem

d()/d(x)(ex)/x

Solution

1. Identify the rule needed for the derivative of a quotient of two functions, which is the quotient rule.

2. Apply the formula for the quotient rule, d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2) where u=ex and v=x

3. Differentiate the individual components: d(ex)/d(x)=ex and d(x)/d(x)=1

4. Substitute these derivatives into the quotient rule formula.

5. Simplify the numerator by factoring out the common term ex

Final Answer

d()/d(x)(ex)/x=(ex*(x−1))/(x2)

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