wrote:
suppose we have

dx/dz = Constant1

Show that

d^2/(dx)^2 =( Constant2 ) d/dz


or (the second derivative with respect to x = Constant2 * the first
derivative with respect to z)

any advice?

First of all, I don't see any partial derivatives there. Nor do I see
any sensible way to interpret some of the derivatives as if you had
written a partial derivative symbol instead of a "d." By the first
equation, you're implying that x is a function of z, so it wouldn't
make sense to vary x and hold z constant. Are you sure there are
partial derivatives involved here, or are you just confused by the fact
that there are multiple variables involved?

Second, assuming none of the derivatives are partial, which is the only
way I can interpret what you wrote, then the statement is wrong.
Let x = z; then the first equation is satisfied. Let the function
being operated on in the second equation be f(z) = z^2. Then the
second equation would imply 2 = Constant2 * (2z).

Are you sure you didn't mean

d/dx =( Constant2 ) d/dz

or

d^2/(dx)^2 =( Constant3 ) d^2/(dz)^2

(neither of which involve partial derivatives) ?

Assuming Constant1 is nonzero, the first would follow immediately from
using the chain rule to find d/dz, and the second follows from the
first.