I have an important exam on Monday and I stumbled upon this problem.

Problem: Calculate the angle (with tan(x) function) between the tangent lines drawn from (-4,1) point to a graph y^2=2*x.

I know that derivative of function represents its tangent line equation, however I cannot seem to implement the given point into the equation since it's out of the domain. Is the correct derivative:

Since the given equation represents a non "1-1" function, divide the graph into two separate graphs (y=sqrt(2*x) and y=-sqrt(2*x)) then dy=1/sqrt(2*x) and dy=-1/sqrt(2*x). I know I did something wrong but not sure what.

I hope somebody can help me. Thanks in advance