Find dy - dx in the following questions-a x-b y2-cos y

Given, ax+by^2=cos y Differentiating both sides w.r.t. x, we get d/dx(ax+by^2)=d/dx(cos y) a+2bydy/dx= sin ydy/dx⇒2bydy/dx+sin ydy/dx= a dy/dx(2by+sin y)= a⇒ ...

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Standard XII

Mathematics

Properties Derived from Trigonometric Identities

Find dy / dx ...

Question

Find $\frac{d y}{d x}$ in the following questions:

$a x + b y^{2} = c o s y$

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Solution

Given, $a x + b y^{2} = c o s y$

Differentiating both sides w.r.t. x, we get

$\frac{d}{d x} (a x + b y^{2}) = \frac{d}{d x} (c o s y)$

$a + 2 b y \frac{d y}{d x} = - s i n y \frac{d y}{d x} \Rightarrow 2 b y \frac{d y}{d x} + s i n y \frac{d y}{d x} = - a$

$\frac{d y}{d x} (2 b y + s i n y) = - a \Rightarrow \frac{d y}{d x} = \frac{- a}{2 b y + s i n y}$

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Find dydxin the following questions: ax+by2=cos y

Given, ax+by2=cos y Differentiating both sides w.r.t. x, we get ddx(ax+by2)=ddx(cos y) a+2bydydx=−sin ydydx⇒2bydydx+sin ydydx=−a dydx(2by+sin y)=−a⇒dydx=−a2by+sin y

Find $\frac{d y}{d x}$ in the following questions:

$a x + b y^{2} = c o s y$