Continuity and Differentiability — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Find $\frac{d y}{d x}$ if sin2 y + cos xy = $\kappa$
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Answer
It is given that sin2 y + cos xy = $\kappa$ Differentiating both sides w.r.t. $x$, we get, $\frac{d}{d x}\left(\sin ^{2} y+\cos x y\right)=\frac{d}{d x}(\kappa)$ $\Rightarrow 2 \sin y \cos y \frac{d y}{d x}-\sin x y\left[y \frac{d}{d x}(x)+x \frac{d y}{d x}\right]=0$ $\Rightarrow 2 \sin y \cos y \frac{d y}{d x}-\sin x y\left[y \cdot 1+x \frac{d y}{d x}\right]=0$ $\Rightarrow 2 \sin y \cos y \frac{d y}{d x}-y \sin x y-x \sin x y \frac{d y}{d x}=0$ $\Rightarrow(2 \sin y \cos y-x \sin x y) \frac{d y}{d x}=y \sin x y$ $\Rightarrow(\sin 2 y-x \sin x y) \frac{d y}{d x}=y \sin x y$ $\Rightarrow \frac{d y}{d x}=\frac{\text { y sin xy }}{(\sin 2 y-x \sin x y)}$
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