Find the Derivative - d/dt f(t)=(sin(t))/t

Problem

d()/d(t)sin(t)/t

Solution

1. Identify the rule needed for differentiation. Since the function is a quotient of two functions, sin(t) and t the quotient rule must be used.

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

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

4. Differentiate the individual components: d(sin(t))/d(t)=cos(t) and d(t)/d(t)=1

5. Substitute these derivatives into the quotient rule formula.

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

Final Answer

d()/d(t)sin(t)/t=(t*cos(t)−sin(t))/(t2)

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