How Can the Derivative of y=3x²ln(x) Be Simplified Further?

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The discussion focuses on finding the derivative of the function y=3x²ln(x) and whether it can be simplified further. Participants clarify that "Inx" refers to the natural logarithm, ln(x), and correct the derivative calculation, noting that dv/dx should be 1/x instead of I/x. The thread also addresses the appropriateness of posting such problems in technical math sections versus homework categories. Ultimately, the conversation emphasizes the importance of accurate notation and proper categorization of math problems. The derivative simplification remains a central question.
anthonyk2013
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y=3x2Inx

u=3x2
v=Inx
du/dx=6x
dv/dx=I/x

y=u*v

dy/dx=(u)(dv/dx)+(v)(du/dx)

dy/dx=(3x2)(I/x)+(Inx)(6x)

Can I simplify this further
 
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anthonyk2013 said:
y=3x2Inx
What is Inx? If you are going by what is on a button on a calculator, that is ln x (LN), for natural logarithm.
anthonyk2013 said:
u=3x2
v=Inx
du/dx=6x
dv/dx=I/x
If v = ln(x), then dv/dx = 1/x, not I/x.
anthonyk2013 said:
y=u*v

dy/dx=(u)(dv/dx)+(v)(du/dx)

dy/dx=(3x2)(I/x)+(Inx)(6x)

Can I simplify this further

Please post homework-type problems in the Homework & Coursework section, not in the technical math sections. I am moving this thread.
 
Mark44 said:
What is Inx? If you are going by what is on a button on a calculator, that is ln x (LN), for natural logarithm.
If v = ln(x), then dv/dx = 1/x, not I/x.


Please post homework-type problems in the Homework & Coursework section, not in the technical math sections. I am moving this thread.

It's not homework!
 
But it's a homework-type problem, so this is where it goes.
 

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