Question

Calculate y'.
xy^4+x^2y=x+3y

Answer 1

have you heard of implicit differentiation ?

Answer 2

yes but i dont get any of the answer choices as i answer it

Answer 3

\[\Huge{xy^4+x^2y=x+3y}\]
\[\Huge{xy(y^3+x)=x+3y}\]
\[\Huge{xy(y^3+x)-x=3y}\]
\[\Huge{x(y(y^3+x)-x)=3y}\]
\[\Huge{\frac{x^2y}{3}(y^4+xy-1)=y}\]

Answer 4

see that isnt one of my answer choices though

Answer 5

\[\large4xy^3y'+y^4+2xy+x^2y'=1+3y'\\
\large 4xy^3y'+x^2y'-3y'=1-2xy-y^4\\
\large y'(4xy^3+x^2-3)=1-2xy-y^4\\
\Large y'=\frac{1-2xy-y^4}{4xy^3+x^2-3}\]
This isn't one of the choices?