The function g is the constant 3 multiplied by the function x2. The derivative of g is 3 multiplied by the derivative of x2:
g ' (x) = 3(x2)' = 3(2x) = 6x.
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):