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

Problem

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

Solution

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

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

3. Calculate the individual derivatives: d(x)/d(x)=1 and d(ln(x))/d(x)=1/x

4. Substitute these values into the product rule formula: x⋅1/x+ln(x)⋅1

5. Simplify the resulting expression by canceling x in the first term.

Final Answer

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

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