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Algebra of Derivatives

Find 𝑑𝑦𝑑𝑥...

Question

Find $\frac{d y}{d x}$ when 𝑥 and 𝑦 are connected by the relation $t a n^{- 1} (x^{2} + y^{2}) = a$

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Solution

Given : $t a n^{- 1} (x^{2} + y^{2}) = a o r x^{2} + y^{2} = t a n a$
Differentiating both sides w.r.t. 𝑥 , We get,
$\frac{d}{d x} (x^{2} + y^{2}) = \frac{d}{d x} (t a n a)$
$\Rightarrow 2 x + 2 y . \frac{d y}{d x} = 0$
$[∵ \frac{d}{d x} (k) = 0, k i s c o n s t a n t]$
$\Rightarrow \frac{d y}{d x} = \frac{- x}{y}$

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Algebra of Derivatives

Standard XII Mathematics

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