# Derivative

The derivative of a function \(f(x)\) is the limit, if any, of the expression

The value of the derivative at \(y\) is typically witten as one of

By repeating the process \(n\) times we recover higher order derivatives, typically written as one of

\[
\frac{f(x+\delta)-f(x)}{\delta}
\]

as \(\delta\) tends to zero.The value of the derivative at \(y\) is typically witten as one of

\[
\frac{\mathrm{d}f}{\mathrm{d}x}\bigg|_y
\;=\;
\frac{\mathrm{d}f}{\mathrm{d}x}(y)
\;=\;
\overset{\cdot}{f}(y)
\;=\;
f^\prime(y)
\]

The derivative represents the rate of change of the function with reprect to its argument or, equivalently if we plot the function as a graph its tangent, or slope.By repeating the process \(n\) times we recover higher order derivatives, typically written as one of

\[
\frac{\mathrm{d}^nf}{\mathrm{d}x^n}\bigg|_y
\;=\;
\frac{\mathrm{d}^nf}{\mathrm{d}x^n}(y)
\;=\;
f^{(n)}(y)
\]