What is the derivative of f(x) = (x^2 + 1)^2 at (1, 4)?

Answer 1

f(x) = (x^2 + 1)^2 

To find the derivative, use the chain rule: d/dx (f(u)) = df/du * du/dx

u = x^2 + 1, du/dx = 2x

So f'(x) = 2(x^2 + 1)*(2x) = 4x^3 + 2x

At x = 1: f' = 4 + 2 = 6