If `f(x)=((a+x)/(b+x))^(a+b+2x)`, prove that, `f'(0) =[2"log"(a)/(b) +(b^(2)-a^(2))/(ab)]((a)/(b))^(a+b)`.

If f(x)= ((a+x)/(b+x))^(a+b+2x) then prove that f'(0)= [2log(a/b)+(b^2-a^2)/(ab)](a/b)^(a+b)

If g(x)=(x-a)/(x)+(x)/(x-b) , prove that, g((a+b)/(2))=(4ab)/(a^2-b^2)

If f(x)=(a(x-b))/(a-b)+(b(x-a))/(b-a) , then prove that f(a) + f(b) = a + b.

If f(x)=a.(x-b)/(a-b)+b.(x-a)/(b-a) , show that, " "f(a)+f(b)=f(a+b) .

If f(x)=e^(x+a) , g(x)=x^(b^2) and h(x)=e^(b^2x) ,show that (g[f(x)])/(h(x))=e^(ab^2)

Prove that : (viii) (log_(a)x)/(log_(ab)x) = 1+log_(a)b .

If a^(2-x).b^(5x)=a^(x+3).b^(3x) , show that x log (b/a)=1/2log a

If f(x)=a(x-b)/(a-b)+b.(x-a)/(b-a) then show that f(a)+f(b)=f(a+b).

"If "f(x)=|{:(x+a^(2),ab,ac),(ab, x+b^(2),bc),(ac,bc, x+c^(2)):}|," then prove that " f'(x)=3x^(2)+2x(a^(2)+b^(2)+c^(2)) .