Question

Find dy/dx by differentiating implicitly
x^2y+3xy^3-x=3

Answer 1

`(\mathrm d)/(\mathrm dx)\left[x^2y+3xy^3-x\right]=(\mathrm d)/(\mathrm dx)[3]`

`2xy+x^2(\mathrm dy)/(\mathrm dx)+3y^3+9xy^2(\mathrm dy)/(\mathrm dx)-1=0`

`(x^2+9xy^2)(\mathrm dy)/(\mathrm dx)=1-2xy-3y^3`

`(\mathrm dy)/(\mathrm dx)=(1-2xy-3y^3)/(x^2+9xy^2)`