Find the Derivative - d/dx 3x natural log of x

Problem

d()/d(x)*3*x*ln(x)

Solution

1. Identify the rule needed for the derivative of a product of two functions, u=3*x and v=ln(x)

2. Apply the product rule, which states that d()/d(x)*u*v=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: (d(3)*x)/d(x)=3 and d(ln(x))/d(x)=1/x

4. Substitute these derivatives into the product rule formula:

3*x⋅1/x+ln(x)⋅3

5. Simplify the expression by canceling x in the first term and rearranging the second term:

3+3*ln(x)

Final Answer

d()/d(x)*3*x*ln(x)=3+3*ln(x)

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