Find the Derivative - d/dx (sin(x))/(x^2)

Problem

d()/d(x)sin(x)/(x2)

Solution

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

2. Assign the variables for the numerator and denominator. Let u=sin(x) and v=x2

3. Differentiate the individual components. Find d(sin(x))/d(x)=cos(x) and d(x2)/d(x)=2*x

4. Substitute these values into the quotient rule formula.

(x2*cos(x)−sin(x)*(2*x))/((x2)2)

5. Simplify the expression by factoring out common terms in the numerator and simplifying the denominator.

(x*(x*cos(x)−2*sin(x)))/(x4)

6. Reduce the fraction by dividing the numerator and denominator by x

(x*cos(x)−2*sin(x))/(x3)

Final Answer

d()/d(x)sin(x)/(x2)=(x*cos(x)−2*sin(x))/(x3)

Want more problems? Check here!