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if y=(x-1) log(x-1) – (x+1) log(x+1) prove that dy/dx=log(x-1/1+x)

if y=(x-1) log(x-1) – (x+1) log(x+1) prove that dy/dx=log(x-1/1+x)

Grade:12

3 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
7 years ago
dy/dx=(x-1)/(x-1)+log(x-1).1 -{(x+1)/(x+1)+log(x+1).1
=1+log(x-1)-1-log(x+1)
=log((x-1)/(x+1))

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty

Riya gupta
11 Points
3 years ago
dy/dx=(x-1)log(x-1)-(x+1)log(x+1)
After solving it using quotient rule
I.e f(x).g(x)=f(x) d/dx g(x) + g(x) d/dx f(x)
 
dy/dx=(1+log(x-1))-(1+log(x+1))
dy/dx=log(x-1)-log(x+1)
 
Now using property {logapq=logap-logaq}
 
Final answer=log(x-1/x+1)=RHS

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