# Covariant derivatives

#### McGravity

##### New member
I understand covariant derivatives which are given in many textbooks, but is there such a thing as a partial covariant derivative, that is the covariant derivative(s) of Z as a function of x and y?

#### Subhotosh Khan

##### Super Moderator
Staff member
I understand covariant derivatives which are given in many textbooks, but is there such a thing as a partial covariant derivative, that is the covariant derivative(s) of Z as a function of x and y?
Yes there is " partial covariant derivative".

Type in those terms in Google and you'll be referred to >1740 sites!

#### yoscar04

##### Junior Member
Take a look at page 207, Gravitation by Misner, Thorne and Wheeler. This book is considered a classic.

#### yoscar04

##### Junior Member

from Tensors, Differential forms and Variational Principles,
by David Lovelock, Hanno Rund.

#### Singleton

##### New member
What are you calling Z?

#### McGravity

##### New member
The actual function was V = r^2 cos(theta) and came in Relativity Demystified (ironic title!) by McMahon

#### McGravity

##### New member
That is a definition but I was hoping for an explanation, which isn't quite the same thing. If I can find how to covariantly differentiate V = r Cos theta that would be a great help.

#### yoscar04

##### Junior Member
That is a definition but I was hoping for an explanation, which isn't quite the same thing. If I can find how to covariantly differentiate V = r Cos theta that would be a great help.
I thought that the covariant derivative for the case of a scalar function coincides with the gradient of it, and when you generalize it to include vectors and tensors you get also the connection coefficients. Am I wrong?

#### McGravity

##### New member
I thought that the covariant derivative for the case of a scalar function coincides with the gradient of it, and when you generalize it to include vectors and tensors you get also the connection coefficients. Am I wrong?
Yes that sounds right but it's just what you would find in any textbook. My problem came from Relativity Demystified (ironic title)

#### yoscar04

##### Junior Member
No that's way above my head. I am a physicist/engineer, not a mathematician
Indeed it is heavy stuff, but standard differential geometry for GR.

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