Multivariate Calculus

D works for partial derivatives—just specify which variable(s) to differentiate:

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D[x^3 z + 2 y^2 x + y z^3, y, z]

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Or use the ∂ symbol:

(Type ESCpdESC for ∂ and CTRL+- for subscript.)

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\!\(
\*SubscriptBox[\(\[PartialD]\), \(x, y\)]\((
\*SuperscriptBox[\(x\), \(2\)] - 2  x\ y + x\ y\ z)\)\)

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Multiple integrals use the same notation as single integrals:

(Type ESCintESC for ∫ and ESCddESC for .)

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\[Integral]\[Integral]\[Integral](x^2 + y^2 + 
      z^2) \[DifferentialD]y \[DifferentialD]x \[DifferentialD]z

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Symbolic results can often be quite complicated:

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\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-2\), \(x\)]\((x\ Sin[
\*SuperscriptBox[\(y\), \(2\)]] + y\ Cos[
\*SuperscriptBox[\(x\), \(2\)]])\) \[DifferentialD]y \
\[DifferentialD]x\)\)

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When this happens, you can always get an approximate output by using the N command:

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N[%, 5]

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