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

Problem

d()/d(x)*x*(x2−1/x)

Solution

1. Distribute the x into the parentheses to simplify the expression before differentiating.

x*(x2−1/x)=x3−x/x

2. Simplify the second term by dividing x by x

x3−1

3. Apply the power rule d(xn)/d(x)=n*x(n−1) to each term of the simplified expression.

d(x3)/d(x)=3*x2

4. Apply the constant rule d(c)/d(x)=0 to the constant term.

d(1)/d(x)=0

5. Combine the results to find the final derivative.

3*x2−0=3*x2

Final Answer

d()/d(x)*x*(x2−1/x)=3*x2

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