Find the Derivative - d/dt (t^2)/(t-1)

Problem

d()/d(t)(t2)/(t−1)

Solution

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

2. Assign the numerator and denominator to variables. Let u=t2 and v=t−1

3. Differentiate the individual components. Find d(t2)/d(t)=2*t and d(t−1)/d(t)=1

4. Substitute these values into the quotient rule formula.

d()/d(t)(t2)/(t−1)=((t−1)*(2*t)−(t2)*(1))/((t−1)2)

5. Expand the terms in the numerator.

(2*t2−2*t−t2)/((t−1)2)

6. Simplify the numerator by combining like terms.

(t2−2*t)/((t−1)2)

Final Answer

d()/d(t)(t2)/(t−1)=(t2−2*t)/((t−1)2)

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