Differentiate log(1-sinx/1+sinx)^1/2 w.r.t. x
 
 
My answer came out to be -secx. Is this right? 

Asked by Udai | 30th Jul, 2016, 06:52: PM

Expert Answer:

log open parentheses square root of fraction numerator 1 minus sin x over denominator 1 plus sin x end fraction end root close parentheses
Let space space y space equals space square root of fraction numerator 1 minus s i n x over denominator 1 plus s i n x end fraction end root

W e space k n o w space t h a t space i f space y space equals space space square root of fraction numerator 1 minus z over denominator 1 plus z end fraction end root space t h e n space fraction numerator d over denominator d z end fraction left parenthesis y right parenthesis space equals space minus fraction numerator y over denominator 1 minus z squared end fraction space space

S o comma
space fraction numerator d over denominator d x end fraction open parentheses l o g y close parentheses equals 1 over y fraction numerator d over denominator d x end fraction open parentheses y close parentheses

equals space 1 over y cross times space open parentheses negative fraction numerator y over denominator 1 minus sin squared x end fraction close parentheses
equals negative fraction numerator 1 over denominator 1 minus sin squared x end fraction
equals negative fraction numerator 1 over denominator cos squared x end fraction
equals negative s e c squared x

Answered by Vijaykumar Wani | 1st Aug, 2016, 11:47: AM

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