- #1

yungman

- 5,755

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I am confused. I never seen derivative of a vector respect to another vector. When I go on the web, the article just show divergence, curl, gradient etc. But not derivative of a vector respect to another vector?

For example what is

[tex]\frac{d(\vec{x}-\vec{x_0})^2}{d \vec{x}} ?[/tex]

For [tex]\vec{x_0}[/tex] is a constant vector.

The book seems to imply:

[tex]\frac{d[(\vec{x}-\vec{x_0})^2]}{d \vec{x}} = 2(\vec{x}-\vec{x_0}) \frac{d \vec{x}}{d \vec{x}} = 2(\vec{x}-\vec{x_0}) [/tex]

I guess I don't know how to do a derivative like this. Can anyone help? I have looked through the multiple variable book and nothing like this. The variable is always scalar. The closest I seen is:

[tex]\int_C \vec{F} \cdot d\vec{r} \;=\; \int_C \vec{F} \cdot \hat{r}dr[/tex]

But this is not exactly what the book discribed.

The only one that is remotely close is Directional Derivative which I don't think so.

For example what is

[tex]\frac{d(\vec{x}-\vec{x_0})^2}{d \vec{x}} ?[/tex]

For [tex]\vec{x_0}[/tex] is a constant vector.

The book seems to imply:

[tex]\frac{d[(\vec{x}-\vec{x_0})^2]}{d \vec{x}} = 2(\vec{x}-\vec{x_0}) \frac{d \vec{x}}{d \vec{x}} = 2(\vec{x}-\vec{x_0}) [/tex]

I guess I don't know how to do a derivative like this. Can anyone help? I have looked through the multiple variable book and nothing like this. The variable is always scalar. The closest I seen is:

[tex]\int_C \vec{F} \cdot d\vec{r} \;=\; \int_C \vec{F} \cdot \hat{r}dr[/tex]

But this is not exactly what the book discribed.

The only one that is remotely close is Directional Derivative which I don't think so.

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