Help!I don't understand this at all >_<

[Akemi]

I have this problem here:

find the equation of the curve that contains the point (1,2) and has slope m=xy^2/2 at each point (x,y) on the curve?

I have the answer and it says:

m=y'= dy/dx = xy^2/2

why the slope equals y',please help >__<

 

[Deleted member 4993]

I have this problem here:

find the equation of the curve that contains the point (1,2) and has slope m=xy^2/2 at each point (x,y) on the curve?

I have the answer and it says:

m=y'= dy/dx = xy^2/2

why the slope equals y',please help >__<

That is the geometric description of y'.

 

[HallsofIvy]

I have this problem here:

find the equation of the curve that contains the point (1,2) and has slope m=xy^2/2 at each point (x,y) on the curve?

I have the answer and it says:

m=y'= dy/dx = xy^2/2

why the slope equals y',please help >__<

What definition have you learned for y', the derivative of y(x)? Many text books use "slope of the tangent line" as the basic definition!