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

Problem

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

Solution

1. Identify the rule needed for differentiation. Since the function is a quotient of two terms, sin(x) and x use the quotient rule.

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

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

4. Differentiate the individual components to find d(sin(x))/d(x)=cos(x) and d(x)/d(x)=1

5. Substitute these derivatives back into the quotient rule formula.

6. Simplify the resulting expression to find the final derivative.

Final Answer

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

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