Hi this is my first question in [Physics.SE] I saw a lot of posts and I liked them. I hope that my question will be answered too.

While I'm solving a problem in vector calculus. I recognized that I need a proof to answer it.

The problem is the following : Calculate the expression of divergence in spherical coordinates $r, \theta, \varphi$ for a vector field $\boldsymbol{A}$ such that its contravariant components $A^i$

Here's my attempts  :

We know that the divergence of a vector field is : $$\mathbf{div\ V}=\nabla_i v^i$$ Notice that $\mathbf{V}$ is the vector field and $\nabla_k v^i$ its covariant derivative, contracting it we obtain the scalar $\nabla_i v^i$.

My questions are how I can apply this to solve the main problem ?

Can I use the developed expression of the covariant derivative? which is : $$\nabla_k v^i=\partial_k v^i+v^j\Gamma_{kj}^i$$

Hi this is my first question in [Physics.SE] I saw a lot of posts and I liked them. I hope that my question will be answered too.

While I'm solving a problem in vector calculus. I recognized that I need a proof to answer it.

The problem is the following: Calculate the expression of divergence in spherical coordinates $r, \theta, \varphi$ for a vector field $\boldsymbol{A}$ such that its contravariant components $A^i$

Here's my attempts:

We know that the divergence of a vector field is : $$\mathbf{div\ V}=\nabla_i v^i$$ Notice that $\mathbf{V}$ is the vector field and $\nabla_k v^i$ its covariant derivative, contracting it we obtain the scalar $\nabla_i v^i$.

My questions are how I can apply this to solve the main problem ?

Can I use the developed expression of the covariant derivative? which is : $$\nabla_k v^i=\partial_k v^i+v^j\Gamma_{kj}^i$$

Hi this is my first question in 'PHYSICS STACKEXCHANGE' I saw a lot of posts and I liked them. I hope that my question will be answered too.

While I'm solving a problem in vector calculus. I recognized that I need a proof to answer it.

The problem is the following : Calculate the expression of divergence in spherical coordinates $r, \theta, \varphi$ for a vector field $\boldsymbol{A}$ such that its contravariant components $A^i$

Here's my attempts :

We know that the divergence of a vector field is : $$\mathbf{div\ V}=\nabla_i v^i$$ Notice that $\mathbf{V}$ is the vector field and $\nabla_k v^i$ its covariant derivative, contracting it we obtain the scalar $\nabla_i v^i$.

My questions are how I can apply this to solve the main problem ?

Can I use the developed expression of the covariant derivative? which is : $$\nabla_k v^i=\partial_k v^i+v^j\Gamma_{kj}^i$$

Hi this is my first question in [Physics.SE] I saw a lot of posts and I liked them. I hope that my question will be answered too.

While I'm solving a problem in vector calculus. I recognized that I need a proof to answer it.

The problem is the following : Calculate the expression of divergence in spherical coordinates $r, \theta, \varphi$ for a vector field $\boldsymbol{A}$ such that its contravariant components $A^i$

Here's my attempts :

We know that the divergence of a vector field is : $$\mathbf{div\ V}=\nabla_i v^i$$ Notice that $\mathbf{V}$ is the vector field and $\nabla_k v^i$ its covariant derivative, contracting it we obtain the scalar $\nabla_i v^i$.

My questions are how I can apply this to solve the main problem ?

Can I use the developed expression of the covariant derivative? which is : $$\nabla_k v^i=\partial_k v^i+v^j\Gamma_{kj}^i$$