1. ## derivative

If x + y = xy

then dy/dx is?

2. Originally Posted by Mr_Green
If x + y = xy

then dy/dx is?
You can solve the equation for y, but it is simpler to use implicit differentiation (which I presume is what they want here.)
$x + y = xy$ <-- Take the derivative.

$1 + \frac{dy}{dx} = y + x \cdot \frac{dy}{dx}$

$\frac{dy}{dx} - x \cdot \frac{dy}{dx} = y - 1$

$(1 - x)\frac{dy}{dx} = y - 1$

$\frac{dy}{dx} = \frac{y - 1}{1 - x}$

Now, if you need a form of dy/dx explicitly in terms of y, then
$x + y = xy$

$y - xy = -x$

$y(1 - x) = -x$

$y = -\frac{x}{1 - x}$

You can either just take the derivative of this (not that hard to do) or plug this expression for y into dy/dx and simplify.

-Dan

3. i was given multiple choice possibilities of

a= 1/(x-1)

b= (y-1)/(x-1)

c= (1-y)/(x-1)

d= x+y-1

e= (2-xy)/y

so if i multiply numerator and denominator by -1, the answer would be C, correct?

4. Originally Posted by Mr_Green
i was given multiple choice possibilities of

a= 1/(x-1)

b= (y-1)/(x-1)

c= (1-y)/(x-1)

d= x+y-1

e= (2-xy)/y

so if i multiply numerator and denominator by -1, the answer would be C, correct?
Yup!

-Dan