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Solution for Find D Y D X in Each of the Following Cases ( X + Y ) 2 = 2 a X Y ? - CBSE (Science) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

Question

Find  $\frac{dy}{dx}$ in each of the following cases $\left( x + y \right)^2 = 2axy$ ?

Solution

$\text{ We have }, \left( x + y \right)^2 = 2axy$

Differentiating with respect to x, we get,

$\Rightarrow \frac{d}{dx} \left( x + y \right)^2 = \frac{d}{dx}\left( 2axy \right)$
$\Rightarrow 2\left( x + y \right)\frac{d}{dx}\left( x + y \right) = 2a\left[ x\frac{d y}{d x} + y\frac{d}{dx}\left( x \right) \right]$
$\Rightarrow 2\left( x + y \right)\left[ 1 + \frac{d y}{d x} \right] = 2a\left[ x\frac{d y}{d x} + y\left( 1 \right) \right]$
$\Rightarrow 2\left( x + y \right) + 2\left( x + y \right)\frac{d y}{d x} = 2ax\frac{d y}{d x} + 2ay$
$\Rightarrow \frac{d y}{d x}\left[ 2\left( x + y \right) - 2ax \right] = 2ay - 2\left( x + y \right)$
$\Rightarrow \frac{d y}{d x} = \frac{2\left[ ay - x - y \right]}{2\left[ x + y - ax \right]}$
$\Rightarrow \frac{d y}{d x} = \left( \frac{ay - x - y}{x + y - ax} \right)$

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Solution Find D Y D X in Each of the Following Cases ( X + Y ) 2 = 2 a X Y ? Concept: Simple Problems on Applications of Derivatives.
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