# What is the derivative of y=6xy?

Dec 8, 2014

Undefined.

#### Explanation:

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

To get this we use the product rule:

$d \frac{\left(u . v\right)}{\mathrm{dx}} = u . \frac{\mathrm{dv}}{\mathrm{dx}} + u \frac{\mathrm{dv}}{\mathrm{dx}}$

$y = 6 x y$

$y ' = 6 \left(x y\right) '$

$y ' = 6 \left(x . \frac{\mathrm{dy}}{\mathrm{dx}} + y \frac{\mathrm{dx}}{\mathrm{dx}}\right)$

$y ' = 6 \left(x y ' + y\right)$

$y ' = 6 x y ' + 6 y$

$y ' \left(1 - 6 x\right) = 6 y$

$y ' = \frac{6 y}{\left(1 - 6 x\right)}$

Since $x = \frac{1}{6}$ then you can see that y' is undefined.

Sep 26, 2017

#### Answer:

$\frac{\mathrm{dy}}{\mathrm{dx}}$ is undefined

#### Explanation:

If $y = 6 x y$
then (after dividing both sides by $y$)
$\textcolor{w h i t e}{\text{XXX}} 1 = 6 x$
or
$\textcolor{w h i t e}{\text{XXX}} x = \frac{1}{6}$

This is a vertical line with an undefined slope.