Math need help..Please Help solve this question. thank you

Question

Given a scalar field Ø(x,y,z)=xy²z.

Find the following at (2,-1,3):

i)grad Ø.

ii)div (grab Ø).

Answer 1

gradØ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k

div(gradØ) = (∂/∂x)(∂Ø/∂x) + (∂/∂y)(∂Ø/∂y) + (∂/∂z)(∂Ø/∂z)

At (2,-1,3):

gradØ = (∂/∂x)i + (∂/∂y)j + (∂/∂z)k

gradØ = (y²z)i + (2xyz)j + (xy²)k

gradØ = [(-1)²(3)]i + [2(2)(-1)(3)]j + [(2)(-1)²]k

gradØ = 3i - 12j + 2k

div(gradØ) = (∂/∂x)(∂Ø/∂x) + (∂/∂y)(∂Ø/∂y) + (∂/∂z)(∂Ø/∂z)

div(gradØ) = (∂/∂x)(y²z) + (∂/∂y)(2xyz) + (∂/∂z)(xy²)

div(gradØ) = 0 + 2xz + 0

div(gradØ) = 2(2)(3)

div(gradØ) = 12

Hope this helped!