D i f f e r e n t i a t e space open parentheses sin space x close parentheses to the power of cos space x end exponent space plus space cos to the power of minus 1 end exponent space fraction numerator 1 minus x squared over denominator 1 plus x squared end fraction space w. r. t. x.

Asked by inderjeet.saluja | 24th Aug, 2014, 05:48: PM

Expert Answer:

y space equals left parenthesis space sin x right parenthesis to the power of cos x end exponent space plus space cos to the power of minus 1 end exponent left parenthesis fraction numerator 1 minus x squared over denominator 1 plus x squared end fraction right parenthesis equals y 1 plus y 2 fraction numerator d y over denominator d x end fraction equals fraction numerator d y 1 over denominator d x end fraction plus fraction numerator d y 2 over denominator d x end fraction................. left parenthesis 1 right parenthesis y 1 equals space left parenthesis space sin x right parenthesis to the power of cos x end exponent t a k i n g space log a r i t h m space o n space b o t h space s i d e s comma log space y 1 space equals space cos x space log space sin x fraction numerator 1 over denominator y 1 end fraction fraction numerator d y 1 over denominator d x end fraction equals space fraction numerator cos x over denominator sin x end fraction minus sin x log space sin x space fraction numerator d y 1 over denominator d x end fraction equals space left parenthesis space sin x right parenthesis to the power of cos x end exponent left square bracket space fraction numerator cos x over denominator sin x end fraction minus sin x log space sin x space right square bracket y 2 equals space space cos to the power of minus 1 end exponent left parenthesis fraction numerator 1 minus x squared over denominator 1 plus x squared end fraction right parenthesis p u t space x space equals space tan space theta y 2 space equals cos to the power of minus 1 end exponent left parenthesis space fraction numerator 1 minus tan squared theta over denominator 1 plus tan squared theta end fraction right parenthesis y 2 equals space cos to the power of minus 1 end exponent left parenthesis cos space 2 theta right parenthesis space equals 2 theta equals space 2 tan to the power of space minus 1 end exponent x fraction numerator d y 2 over denominator d x end fraction equals fraction numerator 2 over denominator 1 plus x squared end fraction H e n c e comma space fraction numerator d y over denominator d x end fraction equals space left parenthesis space sin x right parenthesis to the power of cos x end exponent left square bracket space fraction numerator cos x over denominator sin x end fraction minus sin x log space sin x space right square bracket plus fraction numerator 2 over denominator 1 plus x squared end fraction......... left square bracket f r o m space 1 right square bracket

Answered by Sanjana Dhopatkar | 25th Aug, 2014, 09:41: AM

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