D
 Usage
Notes
 Further Examples
Here is the derivative of  with respect to x. This can be entered as D[Sin[x], x].
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Here is the familiar Chain Rule of first-year calculus.
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This gives the fourth derivative of  .
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Here is the partial derivative  .
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Normally, if you differentiate a function with respect to x, say, Mathematica will treat all other parameters as constants.
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By specifying that t depends upon x, you can get the desired result for such expressions.
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Here are some advanced examples.
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Sometimes the derivative is kept unevaluated until an argument is substituted for which an evaluation can be given.
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Mathematica can also work with vector derivatives. This gives the gradient, which is the first vector derivative of a scalar function. This can be entered as D[f[x, y], {{x, y}, 1}].
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This gives the Hessian, which is the second vector derivative of a scalar function.
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This gives the Jacobian, which is the first vector derivative of a vector function. This can be entered as D[{f[x, y], g[x, y]}, {{x, y}, 1}].
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This gives the third vector derivative of a scalar function.
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This demonstrates a two dimensional version of the chain rule.
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