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# Differentiation

 D[f,x] partial derivative D[f,x,y,...] multiple derivative D[f{x,n}] nth derivative D[f,x,NonConstants->{v1,v2,...}] with the vi taken to depend on x

Partial differentiation operations.

This gives .
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This gives the third derivative.
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You can differentiate with respect to any expression that does not involve explicit mathematical operations.
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D does partial differentiation. It assumes here that y is independent of x.
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If y does in fact depend on x, you can use the explicit functional form y[x]. "The Representation of Derivatives" describes how objects like y'[x] work.
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Instead of giving an explicit function y[x], you can tell D that y implicitly depends on x. D[y, x, NonConstants->{y}] then represents , with y implicitly depending on x.
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 D[f,{{x1,x2,...}}] the gradient of a scalar function f (f/x1, f/x2, ... ) D[f,{{x1,x2,...},2}] the Hessian matrix for f D[f,{{x1,x2,...},n}] the nth-order Taylor series coefficient D[{f1,f2,...},{{x1,x2,...}}] the Jacobian for a vector function f

Vector derivatives.

This gives the gradient of the function x2+y2.
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This gives the Hessian.
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This gives the Jacobian for a vector function.
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