How do you implicitly differentiate y^2+(y-x)^2-y/x^2-3y?

1 Answer
Nov 26, 2017

First expand the brackets to give:
y^2+(y-x)^2-y/x^2-3y
=y^2+y^2-2xy+x^2-y/x^2-3y
=2y^2-2xy+x^2-yxxx^-2-3y

By implicit differentiation (presumably with respect to x here):
d/dx y^a=ay^(a-1)xxdy/dx.
Also using the product rule:
If f(x) = uv, then f'(x)=u'v+uv'

So the original expression differentiates to:
4y^1 dy/dx - 2(xdy/dx+yxx1)+2x^1-(-2x^-3y+x^-2dy/dx)-3y^0dy/dx
=4ydy/dx-2xdy/dx-2y+2x+(2y)/x^3-1/x^2dy/dx