# Derivatives of Unknown Functions

Differentiating a known function gives an explicit result.

Out[1]= | |

Differentiating an unknown function

gives a result in terms of

.

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*Mathematica* applies the chain rule for differentiation, and leaves the result in terms of

.

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Differentiating again gives a result in terms of

,

, and

.

Out[4]= | |

When a function has more than one argument, superscripts are used to indicate how many times each argument is being differentiated.

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This represents

.

*Mathematica* assumes that the order in which derivatives are taken with respect to different variables is irrelevant.

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You can find the value of the derivative when

by replacing

with

.

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| first derivative of a function of one variable |

| n derivative of a function of one variable |

| derivative of a function of several variables, times with respect to variable i |

Output forms for derivatives of unknown functions.