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Mathematics · Ch 18 — Differentiation

Derivatives of Algebraic Functions

18.2.5

Derivatives of Algebraic Functions

A short reference table of algebraic-function derivatives, for quick lookup:

f(x)f′(x)c (constant)0xnnxn−11xn−nxn+1x12x\begin{array}{ll}f(x) & f'(x)\\ \hline c\ (\text{constant}) & 0\\ x^n & nx^{n-1}\\ \dfrac1{x^n} & -\dfrac n{x^{n+1}}\\ \sqrt x & \dfrac1{2\sqrt x}\end{array} …

Table 1Table 9.2.5 — algebraic function derivatives

f(x) -> f'(x)

c -> 0

x^n -> n x^(n-1)

1/x^n -> -n/x^(n+1) …

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