Question

Find the partial derivatives of the following functions at indicated points.

 h(x, y, z) = x sin (xy) + z²x, `(2, pi/4, 1)`

Answer 1

h(x, y, z) = x sin (xy) + z²x

`(delh)/(delx)` = x[y cos (xy)] + sin (xy) + z²

`(delh)/(dely)` = x² cos (xy)

`(delh)/(delz)` = 2zx

At `(2, pi/4, 1)`

`(delh)/(dely) = 2[pi/4 cos ((2pi)/4)] + sin ((2pi)/4) + (1)^2`

= `pi/2 cos  (pi/2) + sin  (pi/2) + 1`

= `pi/2 (0) + 1 + 1`

= 2

`(delh)/(dely) = (2)^2 cos  ((2pi)/4)`

= `4 cos (pi/2)`

= 4(0)

= 0

`(delh)/(delz)` = 2(1)(2)

= 4