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Differential Calculus

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23 Mar 2008 07:57:46 IST

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Calculate Derivative

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$\text {If} \ y = \frac{\sqrt{1+sinx} + \sqrt{1-sinx}} {\sqrt{1+sinx} - \sqrt{1-sinx}} \\ \\ \text{then find} \ \frac{dy}{dx}$

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Abhijith

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Joined: 23 Jan 2007

Posts: 678

23 Mar 2008 08:27:54 IST

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+ if

and - otherwise.

Similarly,

+ if

and '-' otherwise.

Case 1:

If

(Both the mod terms turn out to be positive)

Case 2:

For all other 'x' not belonging to the above interval,

BALGANESH

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Joined: 21 Dec 2007

Posts: 1025

23 Mar 2008 08:30:15 IST

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1+sinx +

1-sinx *

1+sinx +

1-sinx

1+sinx - ^{[ ]}

1-sinx

1+sinx +

1-sinx

[

1+sinx +

1-sinx ]²
(

1+sinx)² - (

1-sinx)²

1+sinx + 1-sinx + 2

1+sinx

1-sinx
1+sinx - 1 + sinx
2+2

1-sin² x
2sinx
y= 1+ IcosxI
sinx
       for 1st and 4th quadrant
differentiating
dy/dx = -sinx (sinx) - (cosx) (1+cosx) / sin²x
         = -sin² x - cos² x -cosx/sin² x
          = -1-cosx/sin² x
           = -cosec² x - cotxcosecx

for 2nd and 3rd quadrant
y = 1-cosx/sinx
dy/dx = sin²x - cosx(1-cosx)/sin²x
         = sin² x - cos x - cos²x / sin²x

Abhijith

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Joined: 23 Jan 2007

Posts: 678

23 Mar 2008 09:08:17 IST

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ganesha1991,

not

BALGANESH

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Joined: 21 Dec 2007

Posts: 1025

23 Mar 2008 09:41:05 IST

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o yes thats right

i'll try to correct

Hari Shankar

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Joined: 28 Feb 2007

Posts: 2173

23 Mar 2008 10:01:26 IST

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nice working Ganesha. and koni of course

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