<P> where X denotes the jth component of X in this coordinate chart . </P> <P> So, the local form of the gradient takes the form: </P> <Dl> <Dd> ∇ f = g i k ∂ f ∂ x k e i . (\ displaystyle \ nabla f = g ^ (ik) (\ frac (\ partial f) (\ partial x ^ (k))) (\ textbf (e)) _ (i).) </Dd> </Dl> <Dd> ∇ f = g i k ∂ f ∂ x k e i . (\ displaystyle \ nabla f = g ^ (ik) (\ frac (\ partial f) (\ partial x ^ (k))) (\ textbf (e)) _ (i).) </Dd>

Can you take the gradient of a vector field