If f(x)= x 1+x and g(x)=f(f(x)) , then g^ (x) is equal to

Step-by-step solution

Given, f(x)= x 1+x and array rlrl and & g(x) & =f(f(x)) & g(x) & =f ( x x+1 ) & = x 1+x 1+ x x+1 & g(x) & = x 2 x+1 array On differentiating both sides w.r.t. x , we get aligned g^ (x) & = (2 x+1) 1-x(2) (2 x+1)^2 & = 1 (2 x+1)^2 aligned