The function g is the constant 3 multiplied by the function x^{2}. The derivative of g is 3 multiplied by the derivative of x^{2}:

g ' (x) = 3(x^{2})' = 3(2x) = 6x.

Example 2

Let f(x) = 4sin(x). What is f ' (x)?

It doesn't matter that we're using f instead of g for the name of the function; the idea is the same. Since f is the constant 4 multiplied by sin(x), the derivative of f is the constant 4 multiplied by the derivative of sin(x):