Find the Derivative - d/dx (x^2-6x+2)/(2x)

Problem

d()/d(x)(x2−6*x+2)/(2*x)

Solution

1. Simplify the expression by dividing each term in the numerator by the denominator to avoid the quotient rule.

(x2−6*x+2)/(2*x)=(x2)/(2*x)−(6*x)/(2*x)+2/(2*x)

2. Reduce the fractions to their simplest form.

x/2−3+1/x

3. Rewrite the terms using power notation to prepare for differentiation.

1/2*x−3+x(−1)

4. Apply the power rule, which states d(xn)/d(x)=n*x(n−1) to each term individually.

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

d()/d(x)*(−3)=0

d()/d(x)*(x(−1))=−1*x(−2)

5. Combine the results and rewrite the negative exponent as a fraction.

1/2−1/(x2)

Final Answer

d()/d(x)(x2−6*x+2)/(2*x)=1/2−1/(x2)

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