Basic Differentiation Rules and Standard Derivatives

Vocabulary flashcards covering the key derivative formulas for standard mathematical functions.

Common Derivatives Table

A reference table summarizing the fundamental derivative rules for constant, power, trigonometric, exponential, and logarithmic functions.

Derivative of a Constant Function $c$

The derivative of any constant function $c$ (including constants like $\pi$ and $e^3$) is $0$.

Power Rule Derivative $x^n$

The derivative of $x^n$ is $n \cdot x^{n-1}$.

Derivative of $\sin(x)$

The derivative of $\sin(x)$ is $\cos(x)$.

Derivative of $\cos(x)$

The derivative of $\cos(x)$ is $-\sin(x)$.

Derivative of $\tan(x)$

The derivative of $\tan(x)$ is $\sec^2(x)$.

Derivative of $\sec(x)$

The derivative of $\sec(x)$ is $\sec(x) \tan(x)$.

Derivative of $\csc(x)$

The derivative of $\csc(x)$ is $-\csc(x) \cot(x)$.

Derivative of $\cot(x)$

The derivative of $\cot(x)$ is $-\csc^2(x)$.

Derivative of $e^x$

The derivative of $e^x$ is $e^x$.

Derivative of Exponential Function $a^x$

The derivative of $a^x$ is $a^x \cdot \ln(a)$.

Derivative of Natural Logarithm $\ln(x)$

The derivative of $\ln(x)$ is $\frac{1}{x}$.

Derivative of Logarithmic Function $\log_a(x)$

The derivative of $\log_a(x)$ is $\frac{1}{x \ln(a)}$.