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Differentiation of Derivatives — Applied Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceApplied MathsDifferentiation of Derivatives1 Mark
Question
If $y=\sqrt{\sin x+y}$, then $\frac{d y}{d x}$ is equal to _________________
✓

Answer

$\frac{\cos x}{2 y-1}$, because
$
\begin{array}{ll}
\text { Given, } & y=\sqrt{\sin x+y} \\
\Rightarrow & y^2=\sin x+y
\end{array}
$
Different with respect to $x$, we have
$\Rightarrow \quad 2 y \frac{d y}{d x}=\cos x+\frac{d y}{d x}$
$\Rightarrow \quad(2 y-1) \frac{d y}{d x}=\cos x$
$\Rightarrow \quad \frac{d y}{d x}=\frac{\cos x}{2 y-1}$.

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