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Calculus Level 3

y = x 2 + 1 x 2 + 1 x 2 + 1 ⋱ y= x^2 + \dfrac{1}{x^2+\dfrac{1}{x^2 +\dfrac{1}{\ddots}}}

Given the equationb above, then ( 2 y − x 2 ) d y d x (2y-x^2)\dfrac{dy}{dx} can be expressed as which of the following expressions?

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2 x y 2xy − 3 x 2 y 3 -3x^2y^3 x 2 y 2 x^2y^2 y x \dfrac{y}{x}

Md Zuhair by Md Zuhair , 20, India

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2 solutions

Tapas Mazumdar
Mar 25, 2017

We can see that

y = x 2 + 1 y ⟹ y 2 − x 2 y + 1 = 0 y = x^2 + \dfrac 1y \implies y^2 - x^2 y + 1 = 0

Thus

y 2 = x 2 y − 1 y^2 = x^2 y - 1

Differentiating both sides w.r.t. x x to get

2 y d y d x = 2 x y + x 2 d y d x ⟹ ( 2 y − x 2 ) d y d x = 2 x y 2y \dfrac{dy}{dx} = 2xy + x^2 \dfrac{dy}{dx} \implies \left( 2y - x^2 \right) \dfrac{dy}{dx} = \boxed{2xy}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

You are the man with all solutiins . Salute . Thanks

Md Zuhair - 4 years, 2 months ago
Hana Wehbi
Mar 25, 2017

Nice problems, keep posting them.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Ya sure. Ill keep psting

Md Zuhair - 4 years, 2 months ago

You may check out the set which is given above in this question . All of it contains nice problems

Md Zuhair - 4 years, 2 months ago

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I will. Thank you.

Hana Wehbi - 4 years, 2 months ago

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