Find the Derivative - d/dx x- natural log of x

Problem

d()/d(x)*(x−ln(x))

Solution

1. Identify the expression as a difference of two terms, x and ln(x)

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

3. Differentiate the first term, x using the power rule.

d(x)/d(x)=1

4. Differentiate the second term, ln(x) using the standard derivative rule for natural logarithms.

d(ln(x))/d(x)=1/x

5. Combine the results to find the final derivative.

Final Answer

d()/d(x)*(x−ln(x))=1−1/x

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