The derivative from the limit definition practice problems
f′(x) as the limit of the difference quotient, worked algebraically. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = 4 - \frac{1}{x} \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = \frac{3}{x + 2} \), then find \( \displaystyle f'(1) \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = 3 x^{2} - 4 x - 4 \), then find \( \displaystyle f'(2) \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = 2 x^{3} - 5 x \), then find \( \displaystyle f'(1) \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = \frac{1}{x^{2}} \), then find \( \displaystyle f'(-1) \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = x^{3} + 4 x \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = - \frac{3}{x - 2} \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = 2 x - 5 \), then find \( \displaystyle f'(2) \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = \frac{1}{x^{2}} \).
Use the limit definition of the derivative to find \( \displaystyle f'(x) \) for \( \displaystyle f(x) = 2 x^{2} + 3 \), then find \( \displaystyle f'(2) \).