Calculus Cheat Sheet (Derivatives)

Definition and Notation

If y = f(x) and f(x) is smooth and continuous (differentiable) at x then:

• m = f ′(a) is the slope of the line tangent to f(a) if f(x) is differentiable at a.
• The equation of the line tangent to f(x) at a is given by:
• f ′(a) is the instantaneous rate of change of f(x) at a.