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A d over a d, naming both the function and the variable differentiated against.
Also known as: d by dx, Leibniz notation, Differential quotient, dy over dx
df/dx is the only common derivative notation that says what is being differentiated and with respect to what, which is why it is the one that survives into multivariable work and into the chain rule, where the apparent cancellation of differentials is a mnemonic that happens to be reliable.
Denotes the derivative of one quantity with respect to another, both named explicitly in the fraction.
Contexts: Mathematics
Is not a fraction, although it behaves like one under the chain rule; treating dx as a quantity in its own right requires machinery the notation does not itself supply.
Contexts: Mathematics
Is Leibniz's and is the reason the integral sign is an elongated S for 'summa' — the two notations were designed as a pair.
Contexts: Mathematics
A lowercase d with a letter, set above a horizontal rule with another lowercase d and letter below it.