If 2 x + 2 y = 2 x + y , then d x d y =

On differentiating 2 x lo g 2 + 2 y lo g 2 ⋅ dx dy = 2 x ⋅ 2 y dx dy ⋅ lo g 2 + 2 y ⋅ 2 x lo g 2 ⇒ 2 x + 2 y dx dy = 2 x + y dx dy + 2 x + y ⇒ dx dy = 2 y − 2 x + y 2 x + y − 2 x ⇒ dx dy = 2 y − 2 x − 2 y 2 x + 2 y − 2 x = − 2 y − x

Mathematics - Differentiation Question with Solution | TestHub

MathematicsDifferentiationDifferentiation of implicit functionsMedium2 minPYQ_2021

MathematicsMediumsingle choice

$If 2^{x} + 2^{y} = 2^{x + y}, then \frac{d y}{d x} =$

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On differentiating $2^{x} lo g 2 + 2^{y} lo g 2 \cdot \frac{dy}{dx} = 2^{x} \cdot 2^{y} \frac{dy}{dx} \cdot lo g 2 + 2^{y} \cdot 2^{x} lo g 2 \Rightarrow 2^{x} + 2^{y} \frac{dy}{dx} = 2^{x + y} \frac{dy}{dx} + 2^{x + y} \Rightarrow \frac{dy}{dx} = \frac{2 ^{x + y} - 2 ^{x}}{2 ^{y} - 2 ^{x + y}} \Rightarrow \frac{dy}{dx} = \frac{2 ^{x} + 2 ^{y} - 2 ^{x}}{2 ^{y} - 2 ^{x} - 2 ^{y}} = - 2^{y - x}$

Stream:BITSATSubject:MathematicsTopic:DifferentiationSubtopic:Differentiation of implicit functions

⏱ 2mℹ️ Source: PYQ_2021

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