Find the Derivative - d/dx (x^2)/(x-1)

Problem

d()/d(x)(x2)/(x−1)

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 variables for the numerator and denominator. Let u=x2 and v=x−1

3. Differentiate the individual components. The derivative of the numerator is d(x2)/d(x)=2*x and the derivative of the denominator is d(x−1)/d(x)=1

4. Substitute these values into the quotient rule formula.

((x−1)*(2*x)−(x2)*(1))/((x−1)2)

5. Expand the terms in the numerator.

(2*x2−2*x−x2)/((x−1)2)

6. Simplify the numerator by combining like terms.

(x2−2*x)/((x−1)2)

Final Answer

d()/d(x)(x2)/(x−1)=(x2−2*x)/((x−1)2)

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