# Math Help - Derivative formular for F(x)=f(x)g(x)

1. ## Derivative formular for F(x)=f(x)g(x)

$F(x) = f(x)g(x)$
$F^1 = f^1 g + g^1 f$
$F^2 = f^2 g + 2 f^1g^1+g^2f$
$F^3=f^3g+3f^2g^1+3f^1g^2+fg^3$
$F^4=f^4g+4f^3g^1+6f^2g^2+4f^1g^3+fg^4$

could you help to find the fomular for

$F^n= ????$

2. Originally Posted by thangbe
$F(x) = f(x)g(x)$
$F^1 = f^1 g + g^1 f$
$F^2 = f^2 g + 2 f^1g^1+g^2f$
$F^3=f^3g+3f^2g^1+3f^1g^2+fg^3$
$F^4=f^4g+4f^3g^1+6f^2g^2+4f^1g^3+fg^4$

could you help to find the fomular for

$F^n= ????$
http://en.wikipedia.org/wiki/Leibniz...d_product_rule)

3. It's just the binomial theorem with derivatives instead of powers.
So the coefficients are ${n \choose k}={n! \over k!(n-k)!}$
and $f^{(0)}=f$.

4. Originally Posted by matheagle
It's just the binomial theorem with derivatives instead of powers.
So the coefficients are ${n \choose k}$
and $f^{(0)}=f$.

thank you