Rules for Differentiation

The Product Rule

What Is the Product Rule?

The product rule tells you how to find the derivative of the product of two functions. It states:

For $y = uv$ the derivative is given by

y' = u'v + v'u

If $y = x \sin(x)$ the derivative is given by

y' = (x \sin(x))' = (x)'\sin(x) + x (\sin(x))'

Using that $(x)'=1$ and $(\sin(x))' = \cos(x)$ , you get

y' = \sin(x) + x\cos(x)

Understood