Find the Derivative - d/dx x(x^2-5/x)

Problem

d()/d(x)*x*(x2−5/x)

Solution

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

x*(x2−5/x)=x3−5

2. Apply the sum rule for derivatives, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(x3−5)=d(x3)/d(x)−d(5)/d(x)

3. Apply the power rule to the first term, where d(xn)/d(x)=n*x(n−1)

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

4. Apply the constant rule to the second term, noting that the derivative of any constant is zero.

d(5)/d(x)=0

5. Combine the results to find the final derivative.

3*x2−0=3*x2

Final Answer

d()/d(x)*x*(x2−5/x)=3*x2

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