How to left align the element when using begin align, not the whole equation?

Question

I am using begin align command and want to left align my equation. I learned that using flalign I can left align the whole equation. But this is not what I need now. I want to left align my equation "componentwisely". The following is what I have typed. and the right hand sides are automatically right-aligned. How can I fix this?

\begin{align*}
\frac{\partial f}{\partial v^j}&=&\frac{\partial f}{\partial u^l}\frac{\partial u^l}{\partial v^j}\\
\frac{\partial^2f}{\partial v^j\partial v^i}&=&\frac{\partial^2 f}{\partial u^l\partial u^m}\frac{\partial u^m}{\partial v^i}\frac{\partial u^l}{\partial v^j}+\frac{\partial f}{\partial u^l}\frac{\partial^2u^l}{\partial v^j\partial v^i}
\end{align*}

Pictorial description. I want to change 1 to appear like 2.

1.(right aligned right hand side)
_________________________
aa= aaaaaaaaaaa

aa=        aaaa
_________________________
2.(left aligned right hand side)
_________________________
aa= aaaaaaaaaaa

aa= aaaa

---

Answer 1

Remove the second & in

&=&

so that it becomes

&=

Code:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
  \begin{align*}
\frac{\partial f}{\partial v^j} &=\frac{\partial f}{\partial u^l}\frac{\partial u^l}{\partial v^j}\\
\frac{\partial^2f}{\partial v^j\partial v^i} &=\frac{\partial^2 f}{\partial u^l\partial u^m}\frac{\partial u^m}{\partial v^i}\frac{\partial u^l}{\partial v^j}+\frac{\partial f}{\partial u^l}\frac{\partial^2u^l}{\partial v^j\partial v^i}
\end{align*}
\end{document}

Always remember that & (the alignment specifier inside align and friends) has right and left alignment pairs i.e., left hand side of & is right aligned and right hand side is left aligned in pairs.