Why Do Different Forms of the Same Equation Yield Different dy/dx Results?

[vikcool812]

I have a relation xy=c² , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c²/x , then dy/dx comes out to be -c²/x² , what's going wrong ?

 

[Office_Shredder]

I have a relation xy=c² , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c²/x , then dy/dx comes out to be -c²/x² , what's going wrong ?

If xy=c², then y=c²/x. So -y/x = -c²/x² You got the same answer, just in a different form

 

[quasar987]

I have a relation xy=c² , if i apply implicit differentiation to both sides i get dy/dx =-y/x , but if i write the same thing as y=c²/x , then dy/dx comes out to be -c²/x² , what's going wrong ?

Nothing since -y/x = -c²/x2 !