Question

How does (1/y)(dy/dt) = (d/dt)ln|y| ?
Can someone please help me?

Answer 1

heard about chain rule ?

Answer 2

Yes, I know the chain rule and I know that (d/dx)In|y| =1/y..

Answer 3

nopes, (d/dx)In|y| =1/y*(dy/dx)

Answer 4

I don't get why the (dy/dx) is there :/

Answer 5

y is the function of x , right ?
ACTUALLY d/dy (ln y)=1/y

Answer 6

to have dx in denominator,
d/dx = (d/dy) (dy/dx)
hence we multiply by dy/dx

Answer 7

got that or should i elaborate ?

Answer 8

\[\frac{d (\ln(y))}{dt}=\frac{d (\ln(y))}{dy}\frac{d y}{dt}\]

Answer 9

@hartnn I understand your explanation but I just don't get how (1/y)(dy/dt) becomes (d/dt)ln|y| . I understand how (d/dt)ln|y| becomes (1/y)(dy/dt) but not the other way around

Answer 10

@henpen Yes, I get it but how does (1/y)(dy/dt) become (d/dt)ln|y| ?

Answer 11

d(lny)/dy=1/y

Answer 12

Oh I see. So I guess you just substitute d(lny)/dy into 1/y then solve it?