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# Multivariate Calculus

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

 In[1]:= ⨯ `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.)
 In[2]:= ⨯ ```\!\( \*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 ``.)
 In[1]:= ⨯ ```\[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:

 In[2]:= ⨯ ```\!\( \*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:

 In[3]:= ⨯ `N[%, 5]`
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QUICK REFERENCE: Calculus `»`