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

Problem

d()/d(x)cos(x)/x

Solution

1. Identify the rule needed for differentiation. Since the expression is a quotient of two functions, apply the quotient rule: d()/d(x)u/v=(vd(u)/d(x)−ud(v)/d(x))/(v2)

2. Assign the numerator and denominator functions. Let u=cos(x) and v=x

3. Differentiate the individual components. The derivative of the numerator is d(cos(x))/d(x)=−sin(x) and the derivative of the denominator is d(x)/d(x)=1

4. Substitute these values into the quotient rule formula.

(x*(−sin(x))−cos(x)*(1))/(x2)

5. Simplify the numerator by multiplying the terms.

(−x*sin(x)−cos(x))/(x2)

Final Answer

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

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