Question

Hi. How many ways to prove the following:
If y"=f".g+2f'g'+2f.g"
then y^13=?

Answer 1

Is that thirteen derivatives?

Answer 2

Let y = fg
then y'= f'g +g'f
then y" = f''g +f'g' + g" f+g'f' = f"g+2f'g'+fg"
Hence I don't know how can you get \(y"= f"g+2f'g +\large{2}fg"\)

Answer 3

There's a name for this: https://en.wikipedia.org/wiki/General_Leibniz_rule