Table of Derivatives and Rules of Differentiation

Vocabulary practice flashcards covering fundamental differentiation rules, operation properties, and basic derivative formulas.

Constant Multiple Rule

The differentiation rule stating that $(c \times f(x))' = c \times (f(x))'$, where $c$ is a constant and $f(x)$ is a differentiable function.

Sum/Difference Rule

The differentiation rule stating that $(f(x) \times g(x))' = f'(x) \times g'(x)$ for differentiable functions $f(x)$ and $g(x)$.

Product Rule

The differentiation rule stating that $(f \times g)' = f' \times g + g' \times f$ for differentiable functions $f$ and $g$.

Quotient Rule

The differentiation rule stating that $\frac{d}{dx}\frac{f}{g} = \frac{f' \times g - f \times g'}{(g)^2}$ for differentiable functions $f$ and $g$.

Chain Rule

The differentiation rule for composite functions stating that $F'(x) = f'(g) \times g'(x)$.

Derivative of a Constant

The rule stating that the derivative of any constant $C$ is zero: $C' = 0$.

Derivative of $x$

The basic derivative formula stating that $(x)' = 1$.

Derivative of Natural Logarithm ($\ln(x)$)

The formula stating that $(\tan(x))' = \frac{1}{x}$.

Chain Rule for Natural Logarithm ($\ln(u)$)

The derivative formula stating that $(\tan(u))' = \frac{1}{u} \times u'$.