Question

if ..differenciate it

Answer 1

\[y=x*\log _{e}\frac{ x }{ 3 }-x\]

Answer 2

d/dx =ln (x/3)

Answer 3

can you show me the steps?

Answer 4

y= x ln (x/3)-x

For x ln (x/3) use product rule
Let u=x, du/dx = 1
v = ln (x/3), dv/dx= 1/x
Apply product rule : u (dv/dx) + v(du/dx)
x*(1/x) + ln(x/3)*1
= 1 + ln(x/3)

dy/dx = 1 + ln(x/3) - 1
= ln (x/3)