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How does one attack a derivative of this type?

$$ \frac{\partial }{\partial (\mathbf{v})} \mathbf{v}^T\mathbf{v} $$

$$ \begin{align} \frac{\partial }{\partial (\mathbf{v})} \mathbf{v}^T\mathbf{v}&=\left(\frac{\partial }{\partial (\mathbf{v})} \mathbf{v}^T\right)\mathbf{v}+ \mathbf{v}^T \frac{\partial }{\partial (\mathbf{v})} \mathbf{v}\\ &=\left(\frac{\partial }{\partial (\mathbf{v})} \mathbf{v}^T\right)\mathbf{v}+ \mathbf{v}^T \end{align} $$

I am uncertain how to treat the part $\left(\frac{\partial }{\partial (\mathbf{v})} \mathbf{v}^T\right)\mathbf{v}$?

Is $\mathbf{v}^T$ constant with respect to $\mathbf{v}$? --- doubtfull.

What is then the derivative of a transpose of a vector?

Anon21
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1 Answers1

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$$\nabla(\mathbf v^T\mathbf v)=\nabla(x^2+y^2+z^2)=2(x\,\mathbf i+y\,\mathbf j+z\,\mathbf k)=2\,\mathbf v.$$