Named in honor of Gottfried Leibniz, a seventeenth century philosopher and mathematician, Leibniz notation is one of the two most popular ways to represent the derivative of a function. (The other representation being Lagrange notation.)
Suppose we have a variable 
that represents 
, a function of the independent variable 
:
The derivative of the function can be written using Leibniz notation as:
![\[\frac{dy}{dx} \quad \text{or} \quad \frac{d}{dx}y\quad \text{or} \quad \frac{d(f(x))}{dx}\]](https://www.neuraldump.net/wp-content/ql-cache/quicklatex.com-4ca1957815fe6fdeb198242501c3c811_l3.png "Rendered by QuickLaTeX.com")
The first two forms can be rewritten in Lagrange notation like so:
![\[\frac{dy}{dx} \equiv \frac{d}{dx}y \equiv y'\]](https://www.neuraldump.net/wp-content/ql-cache/quicklatex.com-15bfcfe9d878573b0c9500751b8ced7d_l3.png "Rendered by QuickLaTeX.com")
And the third form in Lagrange notation is:
![\[\frac{d(f(x))}{dx} \equiv f'(x)\]](https://www.neuraldump.net/wp-content/ql-cache/quicklatex.com-01d6cb2d7a849660c8a10d1be63ae68c_l3.png "Rendered by QuickLaTeX.com")
For higher derivatives, the Leibniz notation for the nth derivative is:
![\[\frac{d^ny}{dx^n} \quad \text{or} \quad \frac{d^n(f(x))}{dx^n}\]](https://www.neuraldump.net/wp-content/ql-cache/quicklatex.com-95a0af5625491375ead0ef62c2e72c35_l3.png "Rendered by QuickLaTeX.com")
For example the second derivate of y or f(x) would be:
![\[\frac{d^2y}{dx^2} \quad \text{or} \quad \frac{d^2(f(x))}{dx^2}\]](https://www.neuraldump.net/wp-content/ql-cache/quicklatex.com-621c302dc986996d58467a7414eac6b1_l3.png "Rendered by QuickLaTeX.com")
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