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Differential Calculus

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 Joined: 1 Sep 2011 Post: 17
17 Sep 2011 12:36:48 IST
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Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Differential Calculus

if x=1/y+1/y+1/y+.................+

then dy/dx = ????

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Joined: 12 May 2011
Posts: 23
25 Sep 2011 13:07:04 IST
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Take x=1/y +1/y +1/y +.... as x= 1/y + x, then differentiate w.r.t.y. Then invert it

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Joined: 23 Jan 2007
Posts: 7958
4 Apr 2012 21:52:52 IST
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$x=\frac{1}{y+\frac{1}{y+\frac{1}{y+....}}}$

$\Rightarrow x=\frac{1}{y+x}$

$\Rightarrow xy+x^{2}=1$

Now differentiate both sides with respect to x :

$x\frac{dy}{dx}+y+2x=0$

$\Rightarrow \frac{dy}{dx}=-\left ( \frac{y}{x}+2 \right )$

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