# Thread: Formula Deriving for 3 differentiable functions

1. ## Formula Deriving for 3 differentiable functions

Extended product rule:
Derive a formula for the derivative of the product fgh of three differentiable functions.

My guess: Using the product rule with a third function (h), I take fgh to be
(f * h') + (g * f') + (h* g')

h' equals the derivative of the function h.

Is that the idea, or do I completely miss the point?

2. Originally Posted by Truthbetold
Extended product rule:
Derive a formula for the derivative of the product fgh of three differentiable functions.

My guess: Using the product rule with a third function (h), I take fgh to be
(f * h') + (g * f') + (h* g')

h' equals the derivative of the function h.

Is that the idea, or do I completely miss the point?
it seems you have missed it. think of it this way. you know the product rule for the scenario when you have two functions, so use that, write the product of 3 functions as the product of two functions and apply the product rule

Let $\displaystyle f,g, \mbox{ and }h$ be functions of $\displaystyle x$

$\displaystyle \frac d{dx}fgh = \frac d{dx}(fg)h = (fg)'h + (fg)h'$

now use the product rule to find $\displaystyle (fg)'$, then expand and simplify