If for a continuous function `f, f(0)=f(1)=0, f'(1)=2` and `g(x)=f(e^x) e^(f(x))` then `g'(0)=`

Suppose for a differentiable function f,f(0)=0,f(1)=1 and f(0)=4=f'(1) If g(x)=f(e^(x))*e^(f(x)) then g'(0) is

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

A continuous function f(x) satisfies the relation f(x)=e^x+int_0^1 e^xf(t)dt then f(1)=

Let f: (-1,1) rarr R be a differentiable function with f(0) = -1 and f'(0) = 1 let g(x) =[f(2f(x)+2)]^2 , then g'(0) =

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=