How can I apply the product rule to products of more than two functions?

Question

loki · Answer

how about like this:

loki · Answer

$$A \left( X \right) * B \left( X \right) *C \left( X \right)$$

anonymous · Answer

okay, I'll try it

anonymous · Answer

$$B(x)*(A \prime(x) * C(x) + C \prime(x) * A(x)) + A(x) * C(x)*B \prime(x)$$

anonymous · Answer

(PQ)' = PQ' + P'Q 
let Q = RS => Q' = RS' + R'S 
So (PRS)' = (PQ)' = PQ' + P'Q = P(RS' + R'S) + P'(RS)  
(PRS)' = PRS' + PR'S + P'RS

This may then be extended to all multiples by taking the 
sum of the derivative of each function, with the terms multiplied by all non-differentiated terms

eg:
(ABCD)' = ABCD' + ABC'D + AB'CD + A'BCD

anonymous · Answer

:bookmark:

thesmartone · Answer

I heard this was the second asked question in Math. x'D