Derivatives in LaTeX
A derivative measures a rate of change; in LaTeX it is written as a fraction with \frac{dy}{dx}, with primes for , or with \partial for partial derivatives.
LaTeX command
\frac{dy}{dx}Not the symbol you meant? Draw it to find the command →
Leibniz notation uses \frac: \frac{dy}{dx} for a first derivative and \frac{d^2y}{dx^2} for a second. Note the exponent goes on the d in the numerator and on the variable in the denominator, not on the whole thing. Lagrange notation is shorter: uses an apostrophe that renders as a prime, and stacks two.
For functions of several variables, swap the straight d for \partial: \frac{\partial f}{\partial x} is a partial derivative. Mixed partials read \frac{\partial^2 f}{\partial x\, \partial y}, where the thin space \, keeps the two differentials from touching. The \partial symbol is a curly d, slanted like an italic letter.
Newton's dot notation, common in mechanics, marks a time derivative with \dot{x} and a second one with \ddot{x}. Some conventions typeset the differential operator upright as \mathrm{d}, giving \frac{\mathrm{d}y}{\mathrm{d}x}; the \mathrm command needs no special package and is supported by KaTeX.
Other forms
\frac{\partial f}{\partial x}partial derivativef'(x)prime notation\dot{x}Newton's dot notationExamples
$\frac{d}{dx}\left(x^2\right) = 2x$an ordinary derivative as an operator
$\frac{d^2y}{dx^2}$a second derivative in Leibniz form
$f'(x) \quad f''(x)$first and second derivatives with primes
$\frac{\partial^2 f}{\partial x\, \partial y}$a mixed second partial derivative
$\dot{x} = \frac{dx}{dt}$Newton's dot notation for velocity
Tips and common mistakes
- For a second derivative write
\frac{d^2y}{dx^2}: the square goes on the d up top and on the x below. - Use
\partial(not a plain d) for partial derivatives; it renders the correct curly symbol. - A prime is just an apostrophe: and work directly, with no need for
\primein ordinary use. \dot{x}and\ddot{x}give first and second time derivatives in Newton's notation.- For an upright differential operator, use
\mathrm{d}, as in\frac{\mathrm{d}y}{\mathrm{d}x}.
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Convert your maths to LaTeX →FAQ
How do I write dy/dx in LaTeX?
Use \frac{dy}{dx}. The \frac command stacks dy over dx with a horizontal bar, which is the standard Leibniz form.
How do I write a second derivative?
In Leibniz notation use \frac{d^2y}{dx^2}. In Lagrange notation use with two apostrophes, which render as a double prime.
How do I write a partial derivative?
Use \partial in place of d: \frac{\partial f}{\partial x}. For higher orders, \frac{\partial^2 f}{\partial x^2}, and for mixed partials \frac{\partial^2 f}{\partial x\, \partial y}.