# How do you find #dy/dx# by implicit differentiation given #xy^3=y+x#?

##### 1 Answer

Feb 21, 2017

#### Explanation:

differentiate each term on both sides

#color(blue)"implicitly with respect to x"#

#"Note differentiate " xy^3" using "color(blue)"product rule"#

#(x.3y^2.dy/dx+y^3 .1)=dy/dx+1#

#rArr3xy^2dy/dx-dy/dx=1-y^3#

#rArrdy/dx(3xy^2-1)=1-y^3#

#rArrdy/dx=(1-y^3)/(3xy^2-1)#