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

5 years ago


Answers : (1)


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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Anil Pannikar

IIT Bombay

5 years ago

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