The derivative of ln^2(x) is 2ln(x)/x. This is different from differentiating ln(x^2) or ln(2x)
F of g of x is a composite function denoted as f(g(x)) or (f ∘ g)(x). It represents the process of combining two functions to form a new one. The symbol '∘' or brackets are used to represent composite functions
The derivative of cos 2x is -2 sin 2x. The derivative can be written as d(cos 2x)/dx or (cos 2x)'
Exponential functions have form f(x) = ax, where a > 0. The derivative of e^2x is 2e^2x. The base 'e' is approximately 2.718
Functions can be explicit (y = x) or implicit (y = x^2 + y^2). Implicit differentiation requires differentiating with respect to x first
Square root can be written as base raised to exponent 1/2. Derivative is 1/2 times base raised to exponent -1/2. Negative exponent means taking reciprocal of positive exponent