Check whether I am correct in Chain Rule

[yungman]

If $r$ is a function of $x,y$, then
$$\delta r= \frac{\partial r}{\partial x}\delta x + \frac{\partial r}{\partial y}\delta y$$
Means

Small change of r = $\left[\frac{\partial r}{\partial x}\right]_{y=k}$ X (Small change of x) + $\left[\frac{\partial r}{\partial y}\right]_{x=k}$ X (Small change of y)

Where $k$ is a constant.

 

[arildno]

Except that your (k,k)-point in the (x,y)-plane should be replaced with the arbitrary (x_0,y_0)-points, that is the constant values of x and y need not be the same.

 

[yungman]

Thanks, I meant k is some constant, I should have specified the two need not be the same.