Find the Derivative - d/dx x(x^2-8/x)

Problem

d()/d(x)*x*(x2−8/x)

Solution

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

x*(x2−8/x)=x3−(8*x)/x

2. Simplify the second term by canceling the x in the numerator and denominator.

x3−8

3. Apply the power rule to differentiate each term of the simplified expression.

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

4. Differentiate the constant term, noting that the derivative of any constant is zero.

d(8)/d(x)=0

5. Combine the results to find the final derivative.

3*x2−0=3*x2

Final Answer

d()/d(x)*x*(x2−8/x)=3*x2

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