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Elementary Differentiation Rules for Basic Functions

The rules that produce derivatives of the building-block functions without returning to the limit definition each time: the power rule, the constant and constant-multiple rules, the sum and difference rules, and the standard derivatives of elementary functions such as $\sin x$, $\cos x$, $e^x$, and $\ln x$.

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Derivatives in Calculus: Differentiating Powers, Trig Functions, and Products using Product Rule

The abstract theory presented defines differentiation rules for polynomial, trigonometric, exponential, and logarithmic functions within the domain of calculus. It establishes formal relationships be…