Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 12-science Answered

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
Asked by ahuja8087 | 17 Mar, 2017, 05:28: PM
answered-by-expert Expert Answer

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

Answered by | 17 Mar, 2017, 05:45: PM
CBSE 12-science - Maths
Asked by sheensvlog | 27 Mar, 2024, 10:15: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by jprathamesh023 | 23 Mar, 2024, 04:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by antra1799 | 18 Mar, 2024, 07:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by nainaadityathakur | 12 Mar, 2024, 01:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by suman0987tewary | 27 Feb, 2024, 03:40: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by hemanthpakkela | 24 Feb, 2024, 04:18: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
t
question image
Asked by rahulkumarphysics1 | 20 Feb, 2024, 09:22: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by sneha47619 | 05 Feb, 2024, 05:24: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 12-science - Maths
Asked by jhaprabhat920 | 05 Feb, 2024, 10:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
Get Latest Study Material for Academic year 24-25 Click here
×