How do you differentiate # f(x)=(e^x+1)*(x+1)*sin(x)# using the product rule?
Treat two of the multiplicands as a single function, then apply the product rule twice.
The product rule states that
To apply it in this case, let's let
Now we can write
So, applying the product rule,
Then we can substitute to put
Now we calculate
Substituting this all in, we have