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)#
