##### Definition5.1.1Leibniz Notation

If \(y=\fe{f}{x}\text{,}\) we say that the derivative of \(y\) with respect to \(x\) is equal to \(\fe{\fd{f}}{x}\text{.}\) Symbolically, we write \(\lz{y}{x}=\fe{\fd{f}}{x}\text{.}\)

While the symbol \(\lz{y}{x}\) certainly looks like a fraction, it is *not* a fraction. The symbol is *Leibniz notation* for the first derivative of \(y\) with respect to \(x\text{.}\) The short way of reading the symbol aloud is “\(d\) \(y\) \(d\) \(x\text{.}\)”

If \(z=\fe{g}{t}\text{,}\) we say that the the derivative of \(z\) with respect to \(t\) is equal to \(\fe{\fd{g}}{t}\text{.}\) Symbolically, we write \(\lz{z}{t}=\fe{\fd{g}}{t}\text{.}\) (Read aloud as “\(d\) \(z\) \(d\) \(t\) equals \(g\) prime of \(t\text{.}\)”)