Question

The product rule

( ) ( ) ( ) ( ) ( ) ( ) fg x f x g x f x g x ′ = + ′ ′
, for all x at which both f and g are
differentiable.

Answer 1

[AI-generated answer — Bot]

This is the product rule of differentiation, which gives the derivative of the product of two functions f(x) and g(x) as the sum of the product of the first function's derivative and the second function, and the product of the second function's derivative and the first function. It is often written as (fg)' = f'g + fg'.