Find the Derivative - d/d@VAR f(x)=(x^2)/(x-1)

Problem

d()/d(x)(x2)/(x−1)

Solution

1. Identify the function as a quotient of two terms, u=x2 and v=x−1 which requires the quotient rule.

2. Recall the quotient rule formula for a function u/v which is (vd(u)/d(x)−ud(v)/d(x))/(v2)

3. Differentiate the numerator u=x2 to get d(u)/d(x)=2*x

4. Differentiate the denominator v=x−1 to get d(v)/d(x)=1

5. Substitute these components into the quotient rule formula.

d()/d(x)(x2)/(x−1)=((x−1)*(2*x)−(x2)*(1))/((x−1)2)

6. Distribute the 2*x in the numerator.

(2*x2−2*x−x2)/((x−1)2)

7. Combine like terms in the numerator to simplify the expression.

(x2−2*x)/((x−1)2)

Final Answer

d()/d(x)(x2)/(x−1)=(x2−2*x)/((x−1)2)

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