A concise lesson on differentiating hyperbolic functions, including essential identities, differentiation formulas, and illustrative examples. It covers key hyperbolic identities such as cosh x + sinh x = e^x and cosh^2 x - sinh^2 x = 1, along with differentiation formulas for sinh u, cosh u, tanh u, coth u, sech u, and csch u. The lesson includes worked examples demonstrating how to apply these formulas to find derivatives of functions involving hyperbolic functions, such as y = sinh x cosh 2x and y = ln sinh x^2, making it a useful resource for students studying calculus and related mathematical concepts. It is designed to help students understand and apply the rules of differentiation to hyperbolic functions effectively, enhancing their problem-solving skills in calculus. Suitable for university-level mathematics courses.