Question

Find all the second partial derivatives. w = u9 + v7

Answer 1

`w_(uu) = 72u^(7)`

`w_(uv) = w_(vu) = 0`

`w_(vv) = 42v^(5)`

Explanation:

We can have the second partial derivatives of w in relation to u, v and uv. So

`w = u^(9) + v^(7)`

`w_(u) = 9u^(8)`

`w_(uu) = 72u^(7)`

`w_(uv) = w_(vu) = 0`

`w_(v) = 7v^(6)`

`w_(vv) = 42v^(5)`