Wolfram Language Fast Introduction for Math Students
Get Started »

Multivariate Calculus

D works for partial derivativesjust specify which variable(s) to differentiate:

In[1]:=
Click for copyable input
D[x^3 z + 2 y^2 x + y z^3, y, z]
Out[1]=

Or use the symbol:

(Type ESCpdESC for and CTRL+- for subscript.)
In[2]:=
Click for copyable input
\!\(
\*SubscriptBox[\(\[PartialD]\), \(x, y\)]\((
\*SuperscriptBox[\(x\), \(2\)] - 2  x\ y + x\ y\ z)\)\)
Out[2]=

Multiple integrals use the same notation as single integrals:

(Type ESCintESC for and ESCddESC for .)
In[1]:=
Click for copyable input
\[Integral]\[Integral]\[Integral](x^2 + y^2 + 
      z^2) \[DifferentialD]y \[DifferentialD]x \[DifferentialD]z
Out[1]=

Symbolic results can often be quite complicated:

In[2]:=
Click for copyable input
\!\(
\*SubsuperscriptBox[\(\[Integral]\), \(-1\), \(1\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-2\), \(x\)]\((x\ Sin[
\*SuperscriptBox[\(y\), \(2\)]] + y\ Cos[
\*SuperscriptBox[\(x\), \(2\)]])\) \[DifferentialD]y \
\[DifferentialD]x\)\)
Out[2]=

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

In[3]:=
Click for copyable input
N[%, 5]
Out[3]=

QUICK REFERENCE: Calculus »