Simplify the following: `1/(1+x^(m-n)+x^(m-p))+(1)/(1+x^(n-p)+x^(n-m))+(1)/(1+x^(n-m)+x^(p-n))`

Solve 1/(1+p^(m-n))+1/(1+p^(n-m))

If y=(1)/(1+x^(n-m)+x^(p-m))+(1)/(1+x^(m-n)+x^(p-m))+(1)/(1+x^(m-p)+x^(n-p)) the (dy)/(dx) is

(m)/(n)x^(2)+(n)/(m)=1-2x

Simplify (i) ((x^(i))/(x^(m)))^((1)/(lm)).((x^(m))/(x^(n)))^((1)/(m)).((x^(n))/(x^(l)))^((1)/(nl)) (ii) ((x^(p))/(x^(q)))^((1)/(ml)).((x^(q))/(x^(r)))^((1)/(mn)).((x^(r))/(x^(p)))^(r+q)

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) at e^m^n^p is equal to: e^(m n p) (b) e^(m n//p) (c) e^(n p//m) (d) none

Differential coefficient of (x^((l+m)/(m-n)))^(1/(n-l))*(x^((m+n)/(n-l)))^(1/(l-m))*(x^((n+l)/(l-m)))^(1/(m-n)) wrt x is

lim_(x rarr0)((2^(m)+x)^((1)/(m))-(2^(n)+x)^((1)/(n)))/(x) is equal to (1)/(m2^(m))-(1)/(n2^(n)) (b) (1)/(m2^(m))+(1)/(n2^(n))(1)/(m2^(-m))-(1)/(n2^(-n))( d) (1)/(m2^(-m))+(1)/(n2^(-n))

(i) lim_(xrarra) (x^(m)-a^(m))/(x^(n)-a^(n)) (ii) lim_(xrarra) ((1+x)^(1//n)-1)/(x)