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Solve the following.
If y = √(sin x + y), then find (dy)/(dx).
If $y = \sqrt{\sin x + y}$, then find $\frac{dy}{dx}$.
Answer
Answer
$y^2 = \sin x + y$
Differentiating with respect to $x$: $2y\frac{dy}{dx} = \cos x + \frac{dy}{dx}$
$\frac{dy}{dx}(2y - 1) = \cos x$
Final answer: $\frac{\cos x}{2y - 1}$