Definition · applies to functions of one variable · also called $f^{\prime}$, $\frac{\mathrm{d}f}{\mathrm{d}x}$

High school

Consider a function $f$ of one variable. The derivative of $f$ is

\[f^{\prime}(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}:\]

the slope of the graph of $f$ at $x$, or the rate at which $f$ changes.

Examples

Worked examples

  • $f(t, x) = t x^2$ : None Undergraduate
    The function $f(t, x) = t x^2$ has no ordinary derivative, because it has two variables.

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