Question

Find the derivative to the equation of the circle ( x^2 + y^2 - 2x + 4y - 4 = 0 )​

Answer 1

`(dy)/(dx) =(1-x)/(y+2)`

Explanation:

We begin with the equation
`x^2+y^2-2x+4y-4=0`

Next, we need to differentiate with respect to x

`2x+2y(dy)/(dx) -2+4(dy)/(dx) =0`

Now we need to solve for
`(dy)/(dx)`

To do this, we need to factor out the
`(dy)/(dx)` and then isolate it.

`2x+2y(dy)/(dx) -2+4(dy)/(dx) =0\\\\2y(dy)/(dx)+4(dy)/(dx)=2-2x\\\\(dy)/(dx)(2y+4)=2-2x\\\\(dy)/(dx)=(2-2x)/(2y+4)\\\\(dy)/(dx)=(1-x)/(y+2)`