If Y = √ X 2 + a 2 Prove that Y D Y D X − X = 0 - Mathematics

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If $y = \sqrt{x^{2} + a^{2}}$ prove that $y \frac{d y}{d x} - x = 0$ ?

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उत्तर

$We have, y = \sqrt{x^{2} + a^{2}}$

Squaring both sides we get,

$y^{2} = x^{2} + a^{2}$

$\Rightarrow 2 y \frac{d y}{d x} = \frac{d}{d x} (x^{2} + a^{2})$

$\Rightarrow 2 y \frac{d y}{d x} = (2 x)$

$\Rightarrow 2 y \frac{d y}{d x} = 2 x$

$\Rightarrow y \frac{d y}{d x} = x$

$\Rightarrow y \frac{d y}{d x} - x = 0$

$Hence proved$

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Simple Problems on Applications of Derivatives

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Q 70 Q 69 Q 71

पाठ 11: Differentiation - Exercise 11.02 [पृष्ठ ३८]

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आरडी शर्मा Mathematics [English] Class 12

पाठ 11 Differentiation
Exercise 11.02 | Q 70 | पृष्ठ ३८

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Simple Problems on Applications of Derivatives

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If Y = √ X 2 + a 2 Prove that Y D Y D X − X = 0 - Mathematics

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If Y = √ X 2 + a 2 Prove that Y D Y D X − X = 0 - Mathematics

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