If f(x) = x^2+1 , g(x) = x+1 x^2+1 , h(x) = 2x - 3 , then f' (h'(g'(x)) ) =

Step-by-step solution

Given f(x) = x^2+1 , differentiating with respect to x gives: f'(x) = 1 2 x^2+1 2x = x x^2+1 Given h(x) = 2x - 3 , differentiating with respect to x gives: h'(x) = 2 Since h'(x) is a constant function, its value is 2 for any input. Therefore, for any x where g'(x) is defined: h'(g'(x)) = 2 We need to find f'(h'(g'(x))) , which simplifies to f'(2) . Substituting x = 2 into the expression for f'(x) : f'(2) = 2 2^2+1 = 2 5