Partial Derivative/Examples/x sine y z

Example of Partial Derivative
Let $\map f {x, y, z} = x \map \sin {y z}$ be a real function of $3$ variables.

Then:


 * $\map {f_3} {a, 1, \pi} = -a$

Proof
By definition, the partial derivative the $3$rd variable $z$ is obtained by holding $1$st and $2$nd ones constant.