Video:Partial derivative

Definition at a point

Generic definition

{{#widget:YouTube|id=wPEMBebMm64}}

For a function of two variables

{{#widget:YouTube|id=vC89LB9mK1g}}{{#widget:YouTube|id=Tj4Nf6xWZh0}}

For a function of multiple variables

{{#widget:YouTube|id=dt-hRS9VNWs}}

Definition as a function

{{#widget:YouTube|id=fvyCAWWFyKA}}

Caveats

Expression for partial derivative depends on all inputs

For further information, refer: Value of partial derivative depends on all inputs

{{#widget:YouTube|id=XYydvau-qIQ}}

Meaning of partial derivative depends on entire coordinate system

{{#widget:YouTube|id=LKwhABs5eBA}}