Definition: The derivative of arcsin(x) equals 1/√(1-x²), valid within the domain [-1,1].

Highlight: Higher-order derivatives are denoted as f'(x), f''(x), f'''(x), and f⁽ⁿ⁾(x) for the nth derivative.

Example: For inverse trigonometric functions, arctan(x) has a domain of all real numbers and range of (-π/2, π/2).

Vocabulary: The notation dy/dx represents the first derivative, while d²y/dx² represents the second derivative.

Definition: The chain rule states that the derivative of a composite function f(g(x)) equals f'(g(x)) multiplied by g'(x).

Example: When differentiating ln(x³), using the chain rule gives us 3/x.

Highlight: For implicit differentiation, remember to include dy/dx whenever differentiating terms containing y.

Vocabulary: Horizontal tangent lines occur when dy/dx = 0, while vertical tangent lines exist when dy/dx is undefined.