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diff(sine-1(1-x2/1+x2)) where x=atany

diff(sine-1(1-x2/1+x2)) where x=atany

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1 Answers

Anil Pannikar AskiitiansExpert-IITB
85 Points
11 years ago

Dear Saurabh,

 

=  1 / √1 - (1-x2/1+x2)2 * diff. (1-x2/1+x2)

= 1 /√ [1 + x4 + 2x2 - (1 + x4 - 2x2)/1 + x4 + 2x2]  * diff. (1-x2/1+x2)

= 1/ [√  4x2 /1 + x4 + 2x2] * diff. (1-x2/1+x2)

= 1/ [2x/1+x2] * diff. (1-x2/1+x2)

= [1 + x2/2 ]* diff. (1-x2/1+x2)

= [1 + x2/2 ]* [ (1+x2)* - 2x - (1-x2)2x ]/(1+x2)2

= -2x/(1+x2)

 

 

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Askiitians Expert

Anil Pannikar

IIT Bombay

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