Find the Derivative - d/dx f(x)=(2x^2-3x+1)/x

Problem

d()/d(x)(2*x2−3*x+1)/x

Solution

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

(2*x2−3*x+1)/x=(2*x2)/x−(3*x)/x+1/x

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

2*x−3+x(−1)

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

(d(2)*x)/d(x)−d(3)/d(x)+d(x(−1))/d(x)

4. Calculate the derivative of each part: the derivative of 2*x is 2 the derivative of a constant −3 is 0 and the derivative of x(−1) is −1*x(−2)

2−0−x(−2)

5. Convert the result back into fraction form for the final expression.

2−1/(x2)

Final Answer

d()/d(x)(2*x2−3*x+1)/x=2−1/(x2)

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