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# Partial Derivatives

Module by: Paul Padley. E-mail the author

Summary: Very brief introduction to the concept of partial differentiation.

## Partial Derivatives

A Partial derivative is defined as the derivative of the function w.r.t. one of the variables while holding the others constant f x = lim Δ x 0 f ( x + Δ x , t ) f ( x , t ) Δ x f x = lim Δ x 0 f ( x + Δ x , t ) f ( x , t ) Δ x f t = lim Δ t 0 f ( x , t + Δ t ) f ( x , t ) Δ t f t = lim Δ t 0 f ( x , t + Δ t ) f ( x , t ) Δ t Some examples: f ( x , t ) = 3 x 2 + x t 2 f ( x , t ) = 3 x 2 + x t 2 f x = 6 x + t 2 f x = 6 x + t 2 f t = 2 x t f t = 2 x t 2 f x 2 = 6 2 f x 2 = 6 2 f t 2 = 2 x 2 f t 2 = 2 x 2 f x t = 2 f t x = 2 t 2 f x t = 2 f t x = 2 t

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