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Question
Find the partial derivatives of the following functions at indicated points.
h(x, y, z) = x sin (xy) + z2x, `(2, pi/4, 1)`
Solution
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
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