Find the Derivative - d/dX (X-1)/X

Problem

d()/d(x)(x−1)/x

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=x−1 and v=x

3. Differentiate the individual components.

d(x−1)/d(x)=1

d(x)/d(x)=1

4. Substitute these values into the quotient rule formula.

(x(1)−(x−1)*(1))/(x2)

5. Simplify the numerator by distributing and combining like terms.

(x−x+1)/(x2)

1/(x2)

Final Answer

d()/d(x)(x−1)/x=1/(x2)

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