True or False: If y = x(ln x), then y' = y/x + 1..........?

Answer 1

True.

Product rule in differentiation is:

if F(x)= f(x)g(x)
then F'=fg' + f'g

let F=y
if f=x, f'=1
if g=ln x, g'=1/x

so y'= F' = [ x (1/x) ] + [1 (ln x)]

y'=1+ ln x

from y=x (ln x), we can rearrange the terms so we have:

ln x= y/x

substitute this in y':

y'=1+ ln x, or
y' = y/x +1

Answer 2

True,

y'=ln(x)+1=(xlnx)/x + 1= y/x +1

First use the product rule then look at the value of y, then plug it in and see if the answer is the same. It is.

Answer 3

false...

y' = 1+ ln x

product rule... that is if you are differentiating with respect to x

Answer 4

True.
y=x (ln x)
=>
ln x=y/x

y'=ln x + 1
=>
y'=y/x + 1

Hence its true.....