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3.5.3 Derivatives of Unknown Functions| Differentiating a known function gives an explicit result. | |
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| Differentiating an unknown function f gives a result in terms of f'. | |
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| Mathematica applies the chain rule for differentiation, and leaves the result in terms of f'. | |
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| Differentiating again gives a result in terms of f, f' and f''. | |
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| 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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D[g[x^2, y^2], x]
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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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D[g[x, y], x, x, y]
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You can find the value of the derivative when  by replacing x with 0. | |
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| f'[x] | first derivative of a function of one variable |  [x] | n derivative of a function of one variable |  [x] | derivative of a function of several variables,  times with respect to variable i |
Output forms for derivatives of unknown functions.
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