How do you differentiate #f(x)=(x^3)(ln3x)(e^x) # using the product rule?
One way to approach this problem is to combine the first two terms (or the last two, your choice) mentally into a single "large" term, and use the Product Rule as you'd expect. When you reach the point of having to take the derivative of the "large" term, you would have to apply the Product Rule to that term off to the side, then substitute the result back in.
The Product Rule can be extended to as many terms as you wish. Simply move one term at a time and take its derivative while keeping the remaining terms intact as-is. You'll note that's essentially what I did above in longhand format. We had 3 "pieces" in the original
Symbolically, this is what I'm noting:
If there were 4 functions multiplied together, it would still hold: