Question

Find dy/dx for 2 + xy = x. Please show your work to receive credit?

Answer 1

`dy/dx = 2/x^2`

Explanation:

You may be tempted to use implicit differentiation here, but since you have a relatively simple equation, it's much easier to solve for `y` in terms of `x`, and then just use normal differentiation. So:

`2 + xy = x`

`=> y = (x-2)/x = 1 - 2/x`

Now we just use a simple power rule:

`=> dy/dx = -(-2x^-2)`

`= 2/x^2`

There you are! Note that you could have used implicit differentiation to solve this, but by doing this we have a derivative that's in terms of just `x`, which is slightly more convenient. However, regardless of the method you use, your answer should be the same.

Hope that helped :)