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 and v=ln(x)

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

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

4. Substitute these derivatives back into the product rule formula.

x⋅1/x+ln(x)⋅1

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

1+ln(x)

Final Answer

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

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