Partial derivatives in terms of both variables

Question

if i have a scalar function as below, i know how to find the partial derivative in terms of x, but can someone gives me some help in understanding how i can take the partial derivative in terms of both variables? Any help is appreciated, thanks in advance

f(x, y) = sin(xy)

What do you mean by the "partial derivative in terms of both variables"? Do you know how to find $\frac{\partial f}{\partial x}$ and $\frac{\partial f}{\partial y}$? — Michael Albanese, Dec 04 '14 at 23:36

score 0 · Accepted Answer · answered Dec 04 '14 at 23:41

0

$$\frac{\partial f}{\partial x} = \cos(xy)\left(\frac{\partial}{\partial x}xy\right) = y\cos(xy)$$

$$\frac{\partial f}{\partial y} = \cos(xy)\left(\frac{\partial}{\partial y}xy\right) = x\cos(xy)$$

answered Dec 04 '14 at 23:41

charlotte

456

Hi @AVERAGE, if this or any answer has solved your question please consider accepting it by clicking the check-mark. This indicates to the wider community that you've found a solution and gives some reputation to both the answerer and yourself. There is no obligation to do this. – charlotte Dec 05 '14 at 00:05

Partial derivatives in terms of both variables

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