Sometimes we need to take a derivative more than once. The second-derivative of a function f (x) is defined to be f ′′(x) = d dx (f ′(x)). In words, the second-derivative is the derivative of the derivative. (We can also define the third-derivative as the derivative of the second- derivative, and so on for higher-derivatives).
For each function below, find the second-derivative of f (x).
(a) f (x) = √x
(b) f (x) = x^2 sin(x)