# Math Help - Partial Derivatives

1. ## [SOLVED]Partial Derivatives

Hi,

For this equation sinxy+sinyz+sinxz=1,
how do I find and?

Thanks

2. Originally Posted by esum0209
Hi,

For this equation sinxy+sinyz+sinxz=1,
how do I find and?

Thanks
This requires you to use implicit partial differentiation. So given $\sin xy+\sin yz+\sin xz=1$, partially differentiate both sides wrt x:

\begin{aligned} &\frac{\partial}{\partial x}\sin xy+ \frac{\partial}{\partial x}\sin yz+\frac{\partial}{\partial x}\sin xz=\frac{\partial}{\partial x}1\\ \implies & y\cos xy+y\frac{\partial z}{\partial x}\cos yz+\left(z+x\frac{\partial z}{\partial x}\right)\cos xz=0\end{aligned}

At this stage, you can now solve for $\dfrac{\partial z}{\partial x}$.

You can do something similar in finding $\dfrac{\partial z}{\partial y}$.

Can you take it from here?

3. Thank you, I get it now