So, what is the difference between cos^3 x, cos x^3 and (cos x)^3 or is there even a difference in between them?
For example, if x= 4, so that (approximately) so that , approximately. Of course, . Of course, so .
Those are three different calculations giving three different answers.
The chain rule! which we can write as , with and . and so that which is very similar to what you have except that it is still in terms of v, not u. To get apply the chain rule again: . Since v= 5x, so .
Of course, you could also do that as one "chain rule": .