straightforwardderived

The term straightforwardderived is a coinage used in mathematical discourse to describe a class of functions or procedures in which the derivative is obtainable by a direct application of standard differentiation rules without requiring advanced techniques such as implicit differentiation, logarithmic differentiation, or complex substitutions. The concept emphasizes that the derivative follows immediately from the explicit form of the function.

In formal terms, a function f is straightforwardderived on an interval if there exists an explicit expression for f and a corresponding expression for f' that can be obtained by a finite, mechanical application of the basic differentiation rules (sum, product, quotient, chain) in a single pass. In practice, many common elementary functions are straightforwardderived.

Examples include polynomials, exponentials, logarithms, trigonometric functions, and their finite compositions. Functions like f(x)=x^2+3x, f(x)=e^{2x}, f(x)=ln(x^2+1) have derivatives obtained by direct rules. In contrast, functions defined implicitly, or defined via inverse operations requiring implicit differentiation, or piecewise definitions with intricate dependence may not be straightforwardderived.

The term is used mainly in informal teaching contexts and in software design to contrast with more involved derivative techniques, such as implicit differentiation, higher-order derivative rules, or automatic differentiation frameworks that propagate derivatives symbolically or numerically. As a concept, straightforwardderived helps categorize functions by the apparent simplicity of their derivative computation.