Find the Derivative - d/dx 1+ natural log of x

Problem

d()/d(x)*(1+ln(x))

Solution

1. Apply the sum rule for differentiation, which states that the derivative of a sum is the sum of the derivatives.

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

2. Differentiate the constant term. The derivative of any constant with respect to x is 0

d(1)/d(x)=0

3. Differentiate the natural log function using the standard derivative rule for ln(x)

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

4. Combine the results to find the final derivative.

0+1/x=1/x

Final Answer

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

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