Find the Derivative - d/dx y=x^2 natural log of 2x

Problem

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

Solution

1. Identify the rule needed for the expression x2*ln(2*x) which is the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Assign the functions u=x2 and v=ln(2*x)

3. Differentiate u to find d(u)/d(x)=2*x

4. Differentiate v using the chain rule: d(ln(2*x))/d(x)=1/(2*x)⋅2=1/x

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

6. Simplify the resulting expression to obtain the final derivative.

Final Answer

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

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