Part 1 - Difference Quotient f(x): = 1 x+4 -1 If h 0, then the difference quotient can be simplified into the form (x+4)(A+Bh) That is: f(x+h) - f(x) h -1 = (x+4)(A+Bh) where the coefficients A, and B can be functions of x or just constant terms. Find these coefficients: A = B= =0 (Note: It's possible for one or more of these coefficients to be 0.) Part 2 - Derivative Use the simplified expression from Part 1 to then calculate the derivative f'(x): f'(x) = lim f(x+h) - f(x) h0 h