Elementary Differentiation and Trigonometric Derivative Rules

A complete set of vocabulary flashcards covering differentiation rules for elementary functions, basic function combinations, and trigonometric functions.

Constant Rule

A differentiation rule stating that $(c)' = 0$, where $c$ is a constant.

Power Rule

A differentiation rule stating that $(x^n)' = n x^{n-1}$, where $n$ is a constant (true for all real $n$).

Constant Multiple Rule

A differentiation rule stating that $[c f(x)]' = c f'(x)$, where $c$ is a constant.

Addition / Subtraction Rules

Differentiation rules stating that $[f(x) \pm g(x)]' = f'(x) \pm g'(x)$.

Product Rule

A differentiation rule stating that $[f(x) \cdot g(x)]' = f'(x) g(x) + f(x) g'(x)$.

Quotient Rule

A differentiation rule stating that $\left[\frac{f(x)}{g(x)}\right]' = \frac{f'(x) g(x) - f(x) g'(x)}{[g(x)]^2}$.

Derivative of Sine

The derivative rule for the sine function, defined as $(\sin(x))' = \cos(x)$.

Derivative of Cosine

The derivative rule for the cosine function, defined as $(\cos(x))' = -\sin(x)$.

Derivative of Tangent

The derivative rule for the tangent function, defined as $(\tan(x))' = \sec^2(x)$.

Derivative of Secant

The derivative rule for the secant function, defined as $(\sec(x))' = \sec(x) \tan(x)$.

Derivative of Cotangent

The derivative rule for the cotangent function, defined as $(\cot(x))' = -\csc^2(x)$.

Derivative of Cosecant

The derivative rule for the cosecant function, defined as $(\csc(x))' = -\csc(x) \cot(x)$.