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

Problem

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

Solution

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

2. Apply the product rule formula, which states that d()/d(x)*(u*v)=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 expression: x⋅1/x+ln(x)⋅1

5. Simplify the resulting expression by canceling x in the first term and removing the multiplier of 1 in the second term.

Final Answer

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

Want more problems? Check here!