Let f and g be differentiable functions satisfying `g(a) = b,g' (a) = 2` and fog =I (identity function). then f' (b) is equal to

If f and g are differentiable functions such that g^(')(a) =2 and g(a) = b and if fog is an identity function then f^(')(b) has the value equal 'to

Let f and g be differentiable functions such that ("fog")'=I . If g'(a)=2 and g(a)=b , then f'(b) equals :

Let f : (-1, 1) to R be a differentiable function with f(0) = -1 and f'(0) = 1 . Let g(x) = [f(2f(x) + 2)]^2 . Then g'(0) is equal to

Let f : (a, b) to R be twice differentiable function such that f(x) = int _(a) ^(x) g (t) dt for a differentiable function g(x) . If f(x) = 0 has exactly five distinct roots in (a,b) , then g(x) g'(x) = 0 has at least