How do you find dydx given 4x2+3xy2−6x2y=y3?
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okkk......first off all ur question is
4x^2+3xy^2-6x^2y=y^3
first of all for solving these kind of problems u need to know about product rule of diffrentiation. well it's the most basic part of diffrentiation.
from question, after diffrentiating we get:-
4×2x +3(y^2+2xydy/dx)-6(2xy+x^2dy/dx)=3y^2dy/dx
after simplyfing:-
8x +3 y^2+6xydy/dx- 12xy-x^2dy/dx = 3y^2dy/dx
( 8x +3 y^2 -12xy)= 3y^2dy/dx + x^2dy/dx - 6xydy/dx
hence dy/dx is equal to:-
dy/dx=( 8x +3 y^2 -12xy) /(3y^2+x^2-6xy)
HOPE THIS WOULD HELP YOU
4x^2+3xy^2-6x^2y=y^3
first of all for solving these kind of problems u need to know about product rule of diffrentiation. well it's the most basic part of diffrentiation.
from question, after diffrentiating we get:-
4×2x +3(y^2+2xydy/dx)-6(2xy+x^2dy/dx)=3y^2dy/dx
after simplyfing:-
8x +3 y^2+6xydy/dx- 12xy-x^2dy/dx = 3y^2dy/dx
( 8x +3 y^2 -12xy)= 3y^2dy/dx + x^2dy/dx - 6xydy/dx
hence dy/dx is equal to:-
dy/dx=( 8x +3 y^2 -12xy) /(3y^2+x^2-6xy)
HOPE THIS WOULD HELP YOU
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