If y = (1)/(x) , then the value of dy 1 + y^ 4 + dx 1 + x^ 4 + 3 is equal to

Correct answer: B. 3 y = (1)/(x) ⇒ (dy)/(dx) = - 1 x^ 2 ⇒ x^ 2 dy + dx = 0 ⇒ x^ 2 dy 1 + x^ 4 + dx 1 + x^ 4 = 0 ⇒ dy 1 x^ 4 + 1 + dx 1 + x^ 4 = 0 ⇒ dy 1 + y^ 4 + dx 1 + x^ 4 = 0 ⇒ dy 1 + y^ 4 + dx 1 + x^ 4 + 3 = 3

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Differentiation

NTA Abhyas 2020 · Mathematics · Differentiation

If y = (1)/(x) , then the value of dy 1 + y^ 4 + dx 1 + x^ 4 + 3 is...

y = \dfrac{1}{x}

, then the value of

\dfrac{dy}{\sqrt{1 + y^{4}}} + \dfrac{dx}{\sqrt{1 + x^{4}}} + 3

is equal to

Options

A $0$
B $3$
C $4$
D $- 3$

Correct answer

B. $3$

Step-by-step solution

y = \dfrac{1}{x} ⇒ \dfrac{dy}{dx} = - \dfrac{1}{x^{2}} ⇒ x^{2}dy + dx = 0

⇒ \dfrac{x^{2}dy}{1 + x^{4}} + \dfrac{dx}{1 + x^{4}} = 0

⇒ \dfrac{dy}{\sqrt{\dfrac{1}{x^{4}} + 1}} + \dfrac{dx}{\sqrt{1 + x^{4}}} = 0

⇒ \dfrac{dy}{\sqrt{1 + y^{4}}} + \dfrac{dx}{\sqrt{1 + x^{4}}} = 0

⇒ \dfrac{dy}{\sqrt{1 + y^{4}}} + \dfrac{dx}{\sqrt{1 + x^{4}}} + 3 = 3

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