Home  18.013A  Chapter 17 


We now address the question: how can we apply the product rule to evaluate such things?
The $\stackrel{\u27f6}{\nabla}$ or "del" operator and the dot and cross product are all linear, and each partial derivative obeys the product rule.
Our first question is: what is $\stackrel{\u27f6}{\nabla}\xb7(f*\stackrel{\u27f6}{v})$ ?
Applying the product rule and linearity we get
And how is this useful?
With it, if the function whose divergence you seek can be written as some function multiplied by a vector whose divergence you know or can compute easily, finding the divergence reduces to finding the gradient of that function, using your information and taking a dot product.
Exercise 17.1 What is the divergence of the vector field $(x,y,z)$ ? Of $(y,x,0)$ ?
