WOLFRAM|DEMONSTRATIONS PROJECT

The Product Rule

f(x)	ln(x)
g(x)	cos(x)

D x (	f(x)	g(x)	) =	g(x)	′ f (x)	+	f(x)	′ g (x)
			=	cos(x)	1 x	+	log(x)	-sin(x)
			=	cos(x) x -log(x)sin(x)

If

f

and

g

are both differentiable at

x

, then the derivative of their product at

x

is given by the product rule shown above. On the graph,

f

is blue,

g

is red,

f(x)g(x)

is purple, and the derivative of

f(x)g(x)

is thick purple.