differenciate using implicit function 2x+4y+sin xy=3


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Question Number 162516 by CM last updated on 30/Dec/21

$d i f f e r e n c i a t e u s i n g i m p l i c i t f u n c t i o n 2 x + 4 y + \sin x y = 3$
Commented by cortano last updated on 30/Dec/21

$\frac{d}{d x} (2 x + 4 y + \sin x y) = \frac{d}{d x} (3)$ $2 + 4 y^{'} + (y + {x y}^{'}) \cos x y = 0$ $4 y^{'} + y \cos x y + {x y}^{'} \cos x y = - 2$ $(4 + x \cos x y) y^{'} = - 2 - y \cos x y$ $y^{'} = - \frac{2 + y \cos x y}{4 + x \cos x y}$
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