Question

If x2 + y2 = sin(x + y), then
dy
dx​

Answer 1

Answer:We know , sin(x+y)= sinx cosy+cosx siny

$x^{2}$+$y^{2}$=sinx cosy+cosx siny

$y^{2}$=sinx cosy+cosx siny-$x^{2}$

differentiating both sides with respect to x

2y$\frac{dy}{dx}$=sinx(-siny×$\frac{dy}{dx}$)+siny(-sinx)-2x

(2y+sinx siny)$\frac{dy}{dx}$=-sinx siny -2x

$\frac{dy}{dx}$=$\frac{-(sinx siny+2x)}{2y+sinx siny}$

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