Find the Derivative - d/dX 3x^2- natural log of x

Problem

d()/d(x)*(3*x2−ln(x))

Solution

1. Apply the sum/difference rule by taking the derivative of each term individually.

d()/d(x)*(3*x2−ln(x))=(d(3)*x2)/d(x)−d(ln(x))/d(x)

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

(d(3)*x2)/d(x)=6*x

3. Apply the derivative rule for natural logarithms to the second term, where the derivative of ln(x) is 1/x

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

4. Combine the results to find the final expression for the derivative.

d()/d(x)*(3*x2−ln(x))=6*x−1/x

Final Answer

d()/d(x)*(3*x2−ln(x))=6*x−1/x

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