Question

If $x^2+2xy+y^2=42$, find $\frac{dy}{dx}.$

Answer 1

We have,

$x^2+2xy+y^2=42$

On differentiating w.r.t $x$, we get

$\frac{d}{dx}(x^2+2xy+y^2)=\frac{d}{dx}\left(42\right)$

$2x+2y+2x\frac{dy}{dx}+2y\frac{dy}{dx}=0$

$x+y+x\frac{dy}{dx}+y\frac{dy}{dx}=0$

$x+y+(x+y)\frac{dy}{dx}=0$

$(x+y)\frac{dy}{dx}=-(x+y)$

$\frac{dy}{dx}=-1$

Hence, this is the answer.