When is the Jacobian of a function a diagonal matrix

[ak123456]

Homework Statement

Let f(x,y,z)=(exp(x),cos(y),sin(z)).Compute the Jacobian J(f) of f . In general ,when will the Jacobian J(g) of a function g(x,y,z) be a diagonal matrix ?

Homework Equations

The Attempt at a Solution

I am not quiet sure about this question
for J(f) i found that
(e^x 0 0)
(0 -siny 0)
(0 0 cosz)
and i think this is already a diagonal matrix

 

[Mark44]

Your Jacobian looks fine to me. The second question was "In general ,when will the Jacobian J(g) of a function g(x,y,z) be a diagonal matrix ?"

What was it about the component functions that gave you all those zeroes off the diagonal?