Diff of this equation

Just checking the answer to a question:

y=(lnx)/x => dy/dx=(1-lnx)/x^2

Done using quotient and u=lnx, du/dx=1/x, v=x, dv/dx=1

\displaystyle x\frac{dy}{dx}+y=\frac{1}{x}

\displaystyle\frac{dy}{dx}=x^{-2}-\frac{y}{x}

\displaystyle\frac{dy}{dx}=x^{-2}-\frac{lnx}{x^2}=\frac{1-lnx}{x^2}

looks fine

\displaystyle x\frac{dy}{dx}+y=\frac{1}{x}

\displaystyle\frac{dy}{dx}=x^{-2}-\frac{y}{x}

\displaystyle\frac{dy}{dx}=x^{-2}-\frac{lnx}{x^2}=\frac{1-lnx}{x^2}

looks fine

Good stuff. I also appreciate the artistic quality of your sig.

Original post by daftndirekt

Good stuff. I also appreciate the artistic quality of your sig.

That's an interesting way to put it. :p:

What’s happening with GCSE, A-level and Btec exams in 2023?

How to prepare for a university interview

What’s happening with GCSE, A-level and Btec exams in 2022?

GCSE Science exams and revision: AQA explains what you need to do