Differentiate a unknown function

Question

I been reading The Theoretical Minimum, and I got to symmetries. A potential is defined as $$ V(q_1,q_2)=V(aq_1-b_2q_2) $$ and, using the Euler-Lagrangian equation $\dot{p_i}=\frac{\partial \mathcal{L}}{\partial q_i}$ the following equations of motion are defined $$ \dot{p_1}=-aV'(aq_1-bq_2) $$ $$ \dot{p_2}=+bV'(aq_1-bq_2) $$ I am having trouble understanding how he gets to $\dot{p_1}$ and $\dot{p_2}$, in particular how $-a$ and $+b$ are obtained.

Answer 1

There should be a minus sign in your $\dot p$ equation.

The derivative of $V$ is obtained using the chain rule.

$$ \partial_{q_i} V(f(q)) = V’(f(q)) \partial_{q_i}f $$