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Mathematics

Product rule - formula in LaTeX

The derivative of a product of two functions. The prime is typed with the plain keyboard apostrophe and LaTeX raises it automatically. A curly apostrophe pasted from a word processor causes a compilation error, so retype it after pasting.

(fg)′=f′g+fg′(fg)' = f'g + fg'

LaTeX code

Open in editor 
$$
(fg)' = f'g + fg'
$$

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What the symbols mean

f,gf, g
differentiable functions
f′,g′f', g'
their derivatives

A math formula - one of the most frequently typed in assignments, lecture notes and calculus or algebra homework.

Worked example

For f(x) = x² and g(x) = sin x. The prime is a plain apostrophe ' typed in math mode, and the second derivative is f''; a curly apostrophe pasted from a word processor breaks compilation.

(x2sin⁡x)′=2xsin⁡x+x2cos⁡x(x^2 \sin x)' = 2x\sin x + x^2\cos x

LaTeX commands in this formula

f'
derivative written with an apostrophe

How to use this formula in LaTeX?

  1. Copy the code with the button above - $$…$$ is centered display math.
  2. Paste it into the CamteX editor, Overleaf or any LaTeX document.
  3. Inside a sentence, use single $…$ instead of double.
  4. The formula works without extra packages.

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