Continuity and Differentiability — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsContinuity and Differentiability2 Marks
Question
Find $\frac{d y}{d x}$ if ax + by2 = cos y
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Answer
It is given that ax + by2 = cos y Differentiating both sides w.r.t. x, we get, $\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ax}+\mathrm{by}^{2}\right)=\frac{\mathrm{d}}{\mathrm{dx}}(\mathrm{cosy})$ $\Rightarrow \frac{d}{d x}(a x)+\frac{d}{d x}\left(b y^{2}\right)=\frac{d}{d x}(\cos y)$ $\Rightarrow a+b \frac{d}{d x}\left(y^{2}\right)=\frac{d}{d x}(\cos y)$ $\Rightarrow a+b \times 2 y \frac{d y}{d x}=-\sin y \frac{d y}{d x}$ $\Rightarrow(2 b y+\sin y) \frac{d y}{d x}=-a$ $\Rightarrow \frac{d y}{d x}=\frac{-a}{(2 b y+\sin y)}$
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