What is the derivative of $y = 6 x y$ $y=6xy$ ?

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Answer 1 · 2014-12-08T21:50:15

Undefined.

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

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.

Answer 2 · 2017-09-26T22:01:47

$dy/dx$ is undefined

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.

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