Find the Derivative - d/dx (sin(x))/x

Problem

d()/d(x)sin(x)/x

Solution

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

2. Apply the quotient rule, which states that d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

3. Assign the variables u=sin(x) and v=x

4. Calculate the individual derivatives d(sin(x))/d(x)=cos(x) and d(x)/d(x)=1

5. Substitute these values into the quotient rule formula.

(x*cos(x)−sin(x)⋅1)/(x2)

6. Simplify the numerator to reach the final expression.

Final Answer

d()/d(x)sin(x)/x=(x*cos(x)−sin(x))/(x2)

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