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

Problem

d()/d(x)(2*x−1)/(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 numerator and denominator functions. Let u=2*x−1 and v=x2

3. Differentiate the individual components.

d(2*x−1)/d(x)=2

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

4. Substitute these values into the quotient rule formula.

(x(2)2−(2*x−1)*(2*x))/((x2)2)

5. Expand the terms in the numerator.

(2*x2−(4*x2−2*x))/(x4)

6. Simplify the numerator by combining like terms.

(2*x2−4*x2+2*x)/(x4)

(−2*x2+2*x)/(x4)

7. Factor out x from the numerator to reduce the fraction.

(x*(−2*x+2))/(x4)

(−2*x+2)/(x3)

Final Answer

d()/d(x)(2*x−1)/(x2)=(2−2*x)/(x3)

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