What is derivative of cosine similarity between two vectors?
I found a paper that refers the derivative of cosine similarity ($\cos=\frac{v_i\cdot{v_j}}{|v_i||v_j|}$) is as below.
$$ \frac{\partial{\cos}}{\partial{v_i}}=\frac{\cos\cdot{v_i}}{\left|v_i\right|^2}+\frac{v_j}{\left|v_i\right|\left|v_j\right|}. $$
There's no detailed explanation in the paper and I couldn't find any derivation of the derivative in internet.
Is the derivation correct? If it's correct, how the derivative is found?
