## fauxshaux 4 years ago How can I apply the product rule to products of more than two functions?

1. loki

2. loki

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

3. fauxshaux

okay, I'll try it

4. fauxshaux

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

(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

6. Ishaan94

:bookmark: