Ask a Doubt
Request a call back

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

JEE Class main Answered

if f left parenthesis x right parenthesis space equals space left parenthesis 1 plus x right parenthesis left parenthesis 1 plus x to the power of 2 space end exponent right parenthesis left parenthesis 1 plus x to the power of 4 right parenthesis................... left parenthesis 1 plus x to the power of 32 right parenthesis space t h e n space f apostrophe left parenthesis x right parenthesis space a t space x equals 1 divided by 2 space i s
Asked by ppavani198 | 19 Dec, 2018, 21:14: PM
answered-by-expert Expert Answer
f(x) = (1+x)(1+x2)(1+x4)(1+x8)(1+x16)(1+x32)
 
log f(x) = log(1+x)+log(1+x2)+log(1+x4)+log(1+x8)+(1+x16)+log(1+x32)
 
By differentiation of above,
begin mathsize 12px style fraction numerator 1 over denominator f left parenthesis x right parenthesis end fraction f apostrophe left parenthesis x right parenthesis space equals space fraction numerator 1 over denominator 1 plus x end fraction plus fraction numerator 2 x over denominator 1 plus x squared end fraction plus fraction numerator 4 x cubed over denominator 1 plus x to the power of 4 end fraction plus fraction numerator 8 x to the power of 7 over denominator 1 plus x to the power of 8 end fraction plus fraction numerator 16 x to the power of 15 over denominator 1 plus x to the power of 16 end fraction plus fraction numerator 32 x to the power of 31 over denominator 1 plus x to the power of 32 end fraction f apostrophe left parenthesis x right parenthesis space space equals space f left parenthesis x right parenthesis space open curly brackets fraction numerator begin display style 1 end style over denominator begin display style 1 plus x end style end fraction plus fraction numerator begin display style 2 x end style over denominator begin display style 1 plus x squared end style end fraction plus fraction numerator begin display style 4 x cubed end style over denominator begin display style 1 plus x to the power of 4 end style end fraction plus fraction numerator begin display style 8 x to the power of 7 end style over denominator begin display style 1 plus x to the power of 8 end style end fraction plus fraction numerator begin display style 16 x to the power of 15 end style over denominator begin display style 1 plus x to the power of 16 end style end fraction plus fraction numerator begin display style 32 x to the power of 31 end style over denominator begin display style 1 plus x to the power of 32 end style end fraction close curly brackets end style
 
to get f '(x) at x=1/2, make the substitution in the above eqn.
Answered by Thiyagarajan K | 20 Dec, 2018, 17:04: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
JEE main - Maths
in how many ways a team of 2 boys and 4 girls selected from 5 boys and 6 girls
Asked by pallavibirangal87 | 08 Dec, 2024, 10:18: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
if a chord of length 18 cm is 12 cm away from the centre then find the distance of 24 cm long chord from the centre
Asked by pritisindra6 | 06 Dec, 2024, 21:04: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
The number of ways in which at least one coin can be selected from 3 coins of one rupee, 4 coins of fifty paise, 5 coins of twenty paise and 6 coins of ten paise is-
Asked by kanishthkumawat | 29 Nov, 2024, 00:23: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
what is range of tan^-1 x
Asked by pawandhayal125 | 06 Oct, 2024, 10:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
what is 2+2
Asked by srishtipra2008 | 28 Sep, 2024, 10:33: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
n arithmetic means are inserted between the numbers 7 and 49. if the sum of these means is 364 then the sum of their squares is
Asked by yogeshsoni575 | 23 Sep, 2024, 23:01: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
consider a dodecagon then number of ways of selecting two triangles which can be made using the vertices of dodecagon so that they do not have a common side.
Asked by sumit.parsudih | 17 Sep, 2024, 22:22: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
the sum of infinite series 1/2(1/3+1/4)-1/4(1/3^2+1/4^2)+1/6(1/3^3+1/4^3)+
Asked by pritamlovevanshi5 | 15 Sep, 2024, 08:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
solve the equation 6x-y+3z=10 , 3x+6y=18 , x+y+5z=-10 by jacobis method with (3,0,-2) as the initial approcimate to the solution
Asked by ganeshbabugottapu7 | 12 Sep, 2024, 18:19: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
find the inverse of a Matrix by using gauss Jordan method -2. 1. 3 A = 0. -1. 1 1. 2. 0
Asked by ganeshbabugottapu7 | 10 Sep, 2024, 07:32: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt