Partial Derivatives

Tangent Plane and Normal Vector

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Clairaut's Theorem:

Suppose that two $n$th order mixed partial derivatives of a function $f$ involve the same differentiation but in different orders. If those partial derivatives are continuous, then the order of differentiation does not matter.

Example

Check Clairaut's Theorem for the partial derivatives $f_{xyz}$ and $f_{zxy}$ for the function $f(x,y,z) = z\sin(2x-y-z)$

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t = 0.00s

Example

Compute $f_{xyz}(x,y,z)$

Compute $f_{zyx}(x,y,z)$

Is Caliraut's Theorem satisfied?