Find the Derivative - d/dx (x^3-1)/x

Problem

d()/d(x)(x3−1)/x

Solution

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

(x3−1)/x=(x3)/x−1/x

2. Rewrite the terms using exponent notation to prepare for the power rule.

x2−x(−1)

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

d(x2)/d(x)−d(x(−1))/d(x)

4. Calculate the derivative of each term.

2*x−(−1)*x(−2)

5. Simplify the signs and rewrite the negative exponent as a fraction.

2*x+1/(x2)

Final Answer

d()/d(x)(x3−1)/x=2*x+1/(x2)

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