How do you implicitly differentiate -1=y^3x-xy+x^4y ?

1 Answer
Mar 23, 2016

dy/dx=(y-y^3-4yx^3)/(3xy^2-x+x^4)

Explanation:

The equation is:

y^3x-xy+x^4y=-1

Differentiating w.r.t. x

We have to apply product rule:

[y^3*d/dxx+xd/dx*y^3]-[x*d/dxy+yd/dx*x]+[x^4*d/dx*y+y*d/dxx^4]=0

[y^3+3xy^2dy/dx]-[x*dy/dx+y]+[x^4*dy/dx+4yx^3]=0

y^3+3xy^2dy/dx-xdy/dx-y+x^4dy/dx+4yx^3=0

3xy^2dy/dx-xdy/dx+x^4dy/dx=-y^3+y-4yx^3

dy/dx[3xy^2-x+x^4]=y-y^3-4yx^3

dy/dx=(y-y^3-4yx^3)/(3xy^2-x+x^4)