Changing differentiated variable in a mixed partial derivative

Question

What operations do I need to perform the following conversion?

$$ \frac{\partial ^2y}{\partial x\partial z} \mapsto \frac{\partial ^2y}{\partial x\partial t} $$

Answer 1

It should be chain rule. From the way you wrote your question, $t$ depends on $z$. So then you should have \begin{align*} \frac{\partial^2 y }{\partial x \partial z} = \frac{\partial^2 y}{\partial x\partial t}\frac{\partial t}{\partial z} \end{align*}

Answer 2

Hint: Use the chain rule by changing your z variable to t