Find the Derivative - d/d@VAR f(x)=x^2 natural log of x

Problem

d()/d(x)*(x2*ln(x))

Solution

1. Identify the function as a product of two terms, u=x2 and v=ln(x) which requires the product rule.

2. Recall the product rule formula for differentiation: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

3. Differentiate the individual components: d(x2)/d(x)=2*x and d(ln(x))/d(x)=1/x

4. Substitute these components into the product rule formula: x2⋅1/x+ln(x)⋅2*x

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

Final Answer

(d(x2)*ln(x))/d(x)=x+2*x*ln(x)

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