# partial differential equations – Length derivative of vectors

Suppose we have 3 vectors satisfying this relation (only 2 are independent we take it as $$p_1,p_3$$.

$$vec{p_1}+vec{p_2}+vec{p_3}=0$$

We want to derive

$$frac{partial vec{p_2}}{partial |p_1|}$$

where $$|vec{p_1}|equiv sqrt{vec{p_1}^2}$$

What is the value of
$$frac{partial vec{p_2}}{partial |p_1|}$$ in terms of $$vec{p_3},vec{p_1}$$?