Archive
17th of March 2017
Mathematics
Q:

If f(x) =open parentheses fraction numerator a plus x over denominator b plus x end fraction close parentheses to the power of a plus b plus x end exponent Prove that f' (0) =open parentheses a over b close parentheses to the power of a plus b space end exponent space open square brackets space L o g space a over b space plus fraction numerator space b squared space minus space a squared space space space over denominator a b end fraction space space space space space space close square brackets

Ahuja8087 Ahuja - CBSE - Class XII Science

Friday, March 17, 2017 at 17:28:PM

A:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis equals open parentheses fraction numerator straight a plus straight x over denominator straight b plus straight x end fraction close parentheses to the power of straight a plus straight b plus straight x end exponent
Take space log space on space both space sides comma space we space get
log space straight f left parenthesis straight x right parenthesis space equals space left parenthesis straight a plus straight b plus straight x right parenthesis space log open parentheses fraction numerator straight a plus straight x over denominator straight b plus straight x end fraction close parentheses
log space straight f left parenthesis straight x right parenthesis space equals space left parenthesis straight a plus straight b plus straight x right parenthesis space open square brackets log open parentheses straight a plus straight x close parentheses minus log left parenthesis straight b plus straight x right parenthesis close square brackets
rightwards double arrow fraction numerator 1 over denominator straight f left parenthesis straight x right parenthesis end fraction straight f apostrophe left parenthesis straight x right parenthesis equals left parenthesis straight a plus straight b plus straight x right parenthesis space straight d over dx space open square brackets log open parentheses straight a plus straight x close parentheses minus log left parenthesis straight b plus straight x right parenthesis close square brackets plus space open square brackets log open parentheses straight a plus straight x close parentheses minus log left parenthesis straight b plus straight x right parenthesis close square brackets straight d over dx left parenthesis straight a plus straight b plus straight x right parenthesis
Simplify space and space then space replace space straight x space by space 0 space througout. end style

Friday, March 17, 2017 at 17:45:PM