1. Partial derivatives.

Hi
I am trying to study partial derivatives but my maths books does not cover it very well-the examples are much too difficult.
I am looking at a previous exam question -can some body tell me if i am on the right track?

Find partial derivatives (df/dx) and (df/dy) -sorry have not worked out how to put proper symbols in yet.

f(x,y)=e^(xy). Cos(y)

i will get the partial derivative when x varies and y is constant first.

Let u=e^(xy) and v=cos(y)

f(x,y)= u. v

Use the product rule.

for the product rule i need du/dx when y is treated as a constant

du/dx=e^(xy).y

I also need dv/dx when x is treated as a constant

dv/dx=0

therefore: the product rule gives df/dx=cos (y^2). e^xy

The is the partial derivative df/dx -i.e when x varies and y is a constant.

Can somebody tell me if this is correct? I will leave the df/dy part until i know my method is correct.

Can recommend a good site that gives easy worked examples that i can follow. Both my maths books do not explain this very well
regards
John

2. Re: Partial derivatives-help!

Originally Posted by celtic1234
Hi
Find partial derivatives (df/dx) and (df/dy) -sorry have not worked out how to put proper symbols in yet.
f(x,y)=e^(xy). Cos(y)
Why not just do it?
$f(x,y)=e^{xy}\cos(y)$

$f_x (x,y) = ye^{xy} \cos (y)$
and
$f_y (x,y) = xe^{xy} \cos (y)-e^{xy}sin(y)$

3. Re: Partial derivatives-help!

you make it look very easy-which it is-maybe i need to look at it simpler
thanks
John