Find the first partial derivatives and evaluate each at the given point.

Question

Function
w = sqrt(5x^2 + y^2 − 4z^2)
Point
(2, −4, 2)

wx(2, −4, 2) =

wy(2, −4, 2) =

wz(2, −4, 2) =

Answer 1

w = (5 x^2 + y^2 - 4 z^2)^.5

dw/dx = (5 x)/(5 x^2 + y^2 - 4 z^2)^.5

dw/dy = y/(5 x^2 + y^2 - 4 z^2)^.5

dw/dz = -4/(5 x^2 + y^2 - 4 z^2)^.5

now just plug in 2, -4, 6

Answer 2

make that -4z...
But I'm sure the student caught the typo.

Answer 3

Thanks, hope so :)