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

Problem

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

Solution

1. Identify the rule needed for the expression 2*x*ln(x) which is the product of two functions u=2*x and v=ln(x)

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

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

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

2*x⋅1/x+ln(x)⋅2

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

2+2*ln(x)

Final Answer

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

Want more problems? Check here!