In this question we will use the definition of the derivative to calculate the derivative of f(x) = By definition, f'(x) is given by the limit of the difference quotient: x+1 f'(x) = lim h-0 f(x+h)-f(x) h Substituting our particular choice of function f(x), this limit becomes: f'(x) = lim h-0 f'(x) = After performing algebraic manipulations and simplifying, we can evaluate the limit to determine f'(x). The result is: