If xy2=ax2+bxy+y2, then find (dy/dx).

Question

If xy2=ax2+bxy+y2, then find (dy/dx). (A) (2ax+by+y2/2xy+bx+2y) (B) (2ax+by-y2/2xy-bx-2y) (C) (ax+by+xy/xy+x2+y2) (D) (2x2+axy+y2/x2+y2+2xy)

Tardigrade Admin · Accepted Answer

We have, xy2 = ax2 + bxy + y2 Differentiating w.r.t. x, we get x⋅2y (dy/dx)+y2=2ax+b(x (dy/dx)+y)+2y (dy/dx) ⇒ (2xy-bx-2y) (dy/dx) =2ax+by-y2 ⇒ (dy/dx)=(2ax+by-y2/2xy-bx-2y)

Q. If $x y^{2} = a x^{2} + b x y + y^{2}$ , then find $\frac{d y}{d x}$ .

$\frac{2 a x + b y + y ^{2}}{2 x y + b x + 2 y}$

$\frac{2 a x + b y - y ^{2}}{2 x y - b x - 2 y}$

$\frac{a x + b y + x y}{x y + x ^{2} + y ^{2}}$

$\frac{2 x ^{2} + a x y + y ^{2}}{x ^{2} + y ^{2} + 2 x y}$

Q. If xy2=ax2+bxy+y2, then find dxdy​.

2xy+bx+2y2ax+by+y2​

2xy−bx−2y2ax+by−y2​

xy+x2+y2ax+by+xy​

x2+y2+2xy2x2+axy+y2​

We have, xy2=ax2+bxy+y2 Differentiating w.r.t. x, we get x⋅2ydxdy​+y2=2ax+b(xdxdy​+y)+2ydxdy​ ⇒(2xy−bx−2y)dxdy​ =2ax+by−y2 ⇒dxdy​=2xy−bx−2y2ax+by−y2​

Q. If $x y^{2} = a x^{2} + b x y + y^{2}$ , then find $\frac{d y}{d x}$ .

$\frac{2 a x + b y + y ^{2}}{2 x y + b x + 2 y}$

$\frac{2 a x + b y - y ^{2}}{2 x y - b x - 2 y}$

$\frac{a x + b y + x y}{x y + x ^{2} + y ^{2}}$

$\frac{2 x ^{2} + a x y + y ^{2}}{x ^{2} + y ^{2} + 2 x y}$