If $x ^ { 2 } y + x y ^ { 2 } = 7$ , then $\frac { d y } { d x } = 2 x y + y ^ { 2 }$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, we need to differentiate the given equation $x^2y + xy^2 = 7$ implicitly with respect to $x$. Differentiating both sides with respect to $x$, we get $2xy + x^2\frac{dy}{dx} + y^2 + 2xy\frac{dy}{dx} = 0$. This does not simplify directly to $\frac{dy}{dx} = 2xy + y^2$, indicating the given statement is false.

If x2y+xy2=7x ^ { 2 } y + x y ^ { 2 } = 7x2y+xy2=7

If $x ^ { 2 } y + x y ^ { 2 } = 7$