Ok, I have a question here, however the problem i have is more simple than the actual question itself, it's a basic math lack of understanding on my part.

Consider the curve defined by:

Find an expression for in terms of x and y, and hence give the equation of the tangent to the curve at the point (x,y) = (1,1)

So, to begin, I make:

then differentiate with respect to X:

giving

Next, differentiate with respect to Y:

giving

Now, I know that the next step is

But I don't understand where the - comes from to make the fraction negative. I know that needs to be inverted to make it into and so moving to the bottom ofthe fraction, but where does the minus sign come from?

Could someone please explain that before we move onto the next step? Thanks