Expanding Brackets with Partial Derivatives

[Zero1010]

Homework Statement

Just need some help to fill in the gaps expanding partial derivative brackets

Relevant Equations

$(y\frac {\partial } {\partial z}(z\frac{\partial f} {\partial x}))$

$(yz\frac {\partial^2 f} {\partial z \partial x} + y\frac{\partial f} {\partial x} \frac{\partial z} {\partial z}))$

Hi,

I just need some (hopefully) quick calculus help.

I have the following:
$(y\frac {\partial } {\partial z}(z\frac{\partial f} {\partial x}))$

After it is expanded this is the solution:
$(yz\frac {\partial^2 f} {\partial z \partial x} + y\frac{\partial f} {\partial x} \frac{\partial z} {\partial z}))$

Could someone please let me know the steps to get to the solution?

Thanks

 

[fresh_42]

It is the product or Leibniz rule of differentiation. The last term is $\dfrac{\partial z}{\partial z}=1$.

 

[Zero1010]

Of course, thanks.

Its been a long day and I just couldn't see it. All I needed was a little nudge.

Thanks for the reply