- #1

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here is what I'm trying to do:

Find

[tex]

\frac{\partial}{\partial x} f(2x, 3y)

[/tex]

First of all, I'm confused by the

[tex]

f(2x, 3y)

[/tex]

How does the function look like? I imagine that it is for example

[tex]

f(x,y) = cos(xy) - sin(3xy^2}

[/tex]

and that therefore

[tex]

f(2x, 3y) = cos(6xy) - sin(54xy^2)

[/tex]

I'm confused, I don't have any good picture of how it might look in real.

Anyway, to accomplish the task:

[tex]

\frac{\partial}{\partial x} f(2x, 3y) = \frac{\partial f}{\partial x}\frac{d(2x)}{dx} + \frac{\partial f}{\partial y}\frac{d(3y)}{dx} = 2\frac{\partial f}{\partial x}

[/tex]

Is it ok? If yes, could you please give an example of this scenario? I mean, how could f(2x, 3y) and f(x,y), respectively, look like so that I could see it with the particular functions?

Thank you very much.