Use Implicit differentiation to find dy/dx of x^2 + xy + y^2 =3
2007-10-12 17:06:58 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
x^2 + xy + y^2 =3
2x+xy'+y+2yy'=0
2x+y'(x+2y)=0
y'(x+2y)=-2x
y'=-2x/(x+2y)
2007-10-12 17:11:08 · answer #1 · answered by ptolemy862000 4 · 0⤊ 1⤋
dy/dx e^y cos x - e^y sin x = cos xy (x dy/dx + y) => dy/dx = (y cos xy + e^y sin x) / (e^y cos x - x cos xy) 2x + 2x dy/dx + 2y - 2y dy/dx + 1 = 0 => dy/dx (2x - 2y) = -2x - 2y - 1 => dy/dx = - (x + y + 0.5)/(x - y) => dy/dx | (3,4) = -7.5/-1 = 7.5
2016-05-22 04:34:22 · answer #2 · answered by ? 3 · 0⤊ 0⤋
d/dx( x² + xy + y²) = 0
2x + y + (dy/dx)(x) + 2y(dy/dx) = 0
(x + 2y)(dy/dx) = - y - 2x
dy/dx = - (2x + y) / (x + 2y)
2007-10-16 07:34:08 · answer #3 · answered by Como 7 · 0⤊ 0⤋
TRUE.
2007-10-12 17:10:52 · answer #4 · answered by montrealgirl108 3 · 0⤊ 0⤋