Find dy/dx of the following question

Question

Find 𝑑𝑦/𝑑𝑥 for the following

𝑥² = 𝑦² + sin 𝑥𝑦

Answer 1

Derivative of x² with respect to x =2x ,

Derivative of y² with respect to x = 2y(dy/dx),

Derivative of Sinx with respect to x = Cosx,

Hence ,

Derivative of sinxy with respect to x = cosxy(y + xdy/dx)

We have used product rule here as d(uv) = udv + vdu.

Therefore answer is,

2x= 2ydy/dx + cosxy(y + xdy/dx)

dy/dx = (2x - ycosxy/2y + x) ans....