Answer :
Answer:
[tex]\frac{dy}{dx} =\frac{1-x}{y+2}[/tex]
Step-by-step explanation:
We begin with the equation [tex]x^2+y^2-2x+4y-4=0[/tex]
Next, we need to differentiate with respect to x
[tex]2x+2y\frac{dy}{dx} -2+4\frac{dy}{dx} =0[/tex]
Now we need to solve for [tex]\frac{dy}{dx}[/tex]
To do this, we need to factor out the [tex]\frac{dy}{dx}[/tex] and then isolate it.
[tex]2x+2y\frac{dy}{dx} -2+4\frac{dy}{dx} =0\\\\2y\frac{dy}{dx}+4\frac{dy}{dx}=2-2x\\\\\frac{dy}{dx}(2y+4)=2-2x\\\\\frac{dy}{dx}=\frac{2-2x}{2y+4}\\\\\frac{dy}{dx}=\frac{1-x}{y+2}[/tex]