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if y = 1/(1+x^n-m + x^p-m )+ 1/(1+x^m-n + x^p-n) + 1/(1+x^m-p + x^n-p) then dy/dx

if y = 1/(1+x^n-m + x^p-m )+ 1/(1+x^m-n + x^p-n)  + 1/(1+x^m-p + x^n-p) then dy/dx
 

Grade:12

2 Answers

Anish Singhal
askIITians Faculty 1192 Points
5 years ago
Let y=u+v+w. and then use log for each term and proceed.
Aditya Gupta
2081 Points
5 years ago
basically anish singhal’s answer is wrong. we need to realise that y=1 and therefore dy/dx=0 
but how is y=1?
1/(1+x^n-m + x^p-m)=x^m/(x^m+x^n+x^p)
1/(1+x^m-n + x^p-n)=x^n/(x^m+x^n+x^p)
1/(1+x^m-p + x^n-p)=x^p/(x^m+x^n+x^p)
so, adding we get
y=(x^m+x^n+x^p)/(x^m+x^n+x^p)
or y=1
so dy/dx=0

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