Product rule

d/dx(uv) = u'v + uv'. For when two functions are multiplied.

When you're differentiating a product of two functions.

Drag the point along the curve

y = x·x·sin(x)at x = 1: slope ≈ 2.22

Product rule

(uv)' = u' v + uv'

Differentiate one factor at a time and add the results — NOT u′v′.

Your turn

Differentiate f(x) = (x³)(eˣ).

Watch out

(uv)′ ≠ u′v′. The derivative of a product is not the product of the derivatives — you need the u′v + uv′ combination.

Product rule

(uv)^{'} = u^{'} v + u v^{'}

Try it

d/dx(x² · sin x)

2x sin x + x² cos x.