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An upright d drawn with a straight stroke, against the curled ∂ of a partial derivative.
Also known as: Total differential, Straight d, Full derivative
The difference between d and ∂ is the entire content of the notation: ∂f/∂x holds every other variable fixed, df/dx does not. In a function whose other variables themselves depend on x, the two give different numbers, and mistaking one for the other is the commonest error in multivariable calculus.
Denotes the derivative accounting for every dependence on the variable, including indirect dependence through other variables.
Contexts: Mathematics
Differs from the partial derivative precisely when the other arguments are themselves functions of the differentiation variable; where they are not, the two coincide.
Contexts: Mathematics
A lowercase d formed from a circle with an upright stroke on its right, contrasted against the hooked curve of the ∂ used for partial derivatives.