What is the Product Rule?

The product rule is used when differentiating two functions that are multiplied by eachother. The formula for the product rule is: 

U (dv/dx) + V (du/dx)    where 'dv/dx' is the differential of the function, V.

For example: 

y=(x² + 3)(2x +5) .... we label the first bracket as U and the second as V.

To find dy/dx we apply the product rule:

U= (x² + 3)      du/dv= 2x as we differentiate any x variable by bringing the power down to the front and then minusing                                       one from the power)

V= (2x+5)        dv/dx= 2

Therefore, applying the product rule gives: 

(x² +3)2 + 2x(2x+5) = 4x² + 10x + 6