partial differentiation.....
$$z=e^x(xcosy-ysiny)$$
$$\frac{\partial{z}}{\partial{x}} = e^x[cosy-0]+e^x[xcosy-ysiny]$$
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this sounds to power rule. $$\frac{\partial{z}}{\partial{x}} = \frac{dz}{dt}\frac{\partial{t}}{\partial{x}}$$
but where is the
$$\frac{\partial{t}}{\partial{x}} = cosy$$
I used product rule to find $$\frac{dz}{dt}e^xt$$. should i consider t as constant?

Question

partial differentiation.....
$$z=e^x(xcosy-ysiny)$$
$$\frac{\partial{z}}{\partial{x}} = e^x[cosy-0]+e^x[xcosy-ysiny]$$
---------------------------------------------------------------------------------
this sounds to power rule. $$\frac{\partial{z}}{\partial{x}} =  \frac{dz}{dt}\frac{\partial{t}}{\partial{x}}$$
but where is the 
$$\frac{\partial{t}}{\partial{x}} = cosy$$
I used product rule to find $$\frac{dz}{dt}e^xt$$. should i consider t as constant?

irishboy123 · Answer

would like to try help but can you post the original question? i get lost half way down, when you introduce 't'. not sure what you are actually trying to do. that said, i suspect the first page of this will get you sorted!! http://wwwf.imperial.ac.uk/~jdg/AECHAIN.PDF good luck!

anonymous · Answer

Question : $$z=e^x(xcosy-ysiny)$$ prove $$\frac{\partial^2{z}}{\partial{x^2}} + \frac{\partial^2{z}}{\partial{y^2}}$$