Originally Posted by

**isp_of_doom** Hi all. I've been having problems with the question below.

$\displaystyle z = sin(xyz) + xln(yz)$

find

$\displaystyle \frac{\partial z}{\partial x}$

I've tried two differentiation methods:

**First**

$\displaystyle \frac{\frac{\partial T} {\partial x}}{\frac{\partial T}{\partial z}}$

which generally gives me:

$\displaystyle \frac{yzcos(xyz) + ln(yz)}{xycos(xyz) + \frac{xy}{yz}}$

I'm not 100% sure about that though. Especially differentiating $\displaystyle \frac {\partial T}{\partial z}$ (the denominator of $\displaystyle \frac{\frac{\partial T} {\partial x}}{\frac{\partial T}{\partial z}}$)

__Secondly__

I dont know the name of this differentiation method or how to describe it, but essentially you differentiate as normal - with respect to x, treating y as a constant.

This time, however, also add $\displaystyle \frac{\partial z}{\partial x}$ whenever you encounter a $\displaystyle z$. Or is it whenever you differentiate $\displaystyle z$? Or is it when $\displaystyle z$ is left from differentiating $\displaystyle x$ - as in $\displaystyle z$ was a coefficient of $\displaystyle x$? As you can see this is where my confusion comes in.

If anyone can confirm or help me with this I would appreciate it. Thanks.