Question

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

Answer 1

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.

Answer 2

`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.