What is the derivative of #y=6xy#?

2 Answers
Dec 8, 2014

Answer:

Undefined.

Explanation:

#y'=(6y)/((1-6x)#

To get this we use the product rule:

#d((u.v))/(dx)=u.(dv)/(dx)+u(dv)/(dx)#

#y=6xy#

#y'=6(xy)'#

#y'=6(x.(dy)/(dx)+y(dx)/(dx))#

#y'=6(xy'+y)#

#y'=6xy'+6y#

#y'(1-6x)=6y#

#y'=(6y)/((1-6x))#

Since #x=1/6# then you can see that y' is undefined.

Sep 26, 2017

Answer:

#dy/dx# is undefined

Explanation:

If #y=6xy#
then (after dividing both sides by #y#)
#color(white)("XXX")1=6x#
or
#color(white)("XXX")x=1/6#

This is a vertical line with an undefined slope.