Suppose that f is a function given as f x follows 1 x 7 We will compute the derivative of fat x 5 as First we compute and simplify the expression f 5 h f 5 h f 5 lim h 0 5 and x 5 h Then we compute and simplify the difference quotient between a f 5 h f 5 h The derivative of the function at x is the limit of the difference quotient as h approaches zero f 5 h f 5 h