Find the Derivative - d/dx x^2-8 natural log of x

Problem

d()/d(x)*(x2−8*ln(x))

Solution

1. Apply the sum/difference rule to differentiate each term of the expression separately.

d()/d(x)*(x2−8*ln(x))=d(x2)/d(x)−(d(8)*ln(x))/d(x)

2. Apply the power rule to the first term, where the derivative of xn is n*x(n−1)

d(x2)/d(x)=2*x

3. Apply the constant multiple rule and the derivative rule for natural logarithms to the second term, where d(ln(x))/d(x)=1/x

(d(8)*ln(x))/d(x)=8⋅1/x

4. Combine the results to find the final derivative.

d()/d(x)*(x2−8*ln(x))=2*x−8/x

Final Answer

d()/d(x)*(x2−8*ln(x))=2*x−8/x

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