And Plato, I typed in the second problem into that website and it said:
This is what I typed into the search box:
derivative of (x^3+1) ^tan x
Also, you could do this,
Now we can implicitly differentiate the left side and apply the product rule to the right side. Should clear everything up.
is true only for b a constant.
(Note the , not u(x). What you wrote:
" is not true even for b a constant.)
To differentiate use the fact that as Allencuz suggested.
There are two common errors made in differentiating something like :
1) Treat the base as a constant: .
2) Treat the exponent as a constant: .
The interesting thing is that the correct derivative is the sum of those errors!