If x+y=sinx+y then dydx= - Sri Chaitanya Infinity Learn Best Online Courses for NCERT Solutions, CBSE, ICSE, JEE, NEET, Olympiad and Class 6 to 12

Solution:

Given $x + y = \sin (x + y)$

Differentiate both sides

$\begin{matrix} 1 + \frac{d y}{d x} = \cos (x + y) \frac{d}{d x} (x + y) \\ 1 + \frac{d y}{d x} = \cos (x + y) (1 + \frac{d y}{d x}) \\ 1 + \frac{d y}{d x} - \cos (x + y) (1 + \frac{d y}{d x}) = 0 \\ (1 + \frac{d y}{d x}) (1 - \cos (x + y)) = 0 \end{matrix}$

It implies $1 + \frac{d y}{d x} = 0 \Rightarrow \frac{d y}{d x} = - 1$

If $x + y = \sin (x + y)$ then $\frac{d y}{d x} =$

Solution:

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