Question

Letf(x,y,z)=x+ln(2y+3z^2)
compute ∂2f/∂y∂x

Answer 1

You can differentiate in any order, so do the easiest first:
df/dx = 1 + 0.
So df/dxdy = 0.

done

Answer 2

i thought df/dy was2/2y+3z^2?

Answer 3

It is, but you can differentiate with respect to x first. You can check it by differentiating df/dy with respect to x. You still get zero.

Answer 4

so then Letf(x,y,z)=x+ln(2y+3z^2)
compute ∂^3f/∂y∂x∂z is 0 to?

Answer 5

Yes

Answer 6

This website will differentiate stuff like this
http://www.wolframalpha.com

input it like this
http://www.wolframalpha.com/input/?i=differentiate+x%2Bln%282y%2B3z^2%29+with+respect+to+x