Correct. Basically the chain rule is used when you have a function of a function. In reality that just means that there are brackets somewhere. So all of these can be differentiated using the chain rule:
(3x2+2)3e(3x)sin(x2)Chain rule in words : Make a substitution for the stuff in the brackets then differentitate what you have now and then multiply by the derivative of the stuff in the brackets.
So
(3x2+2)3 :
Start by differentiating
t3 which is
3t2 then multiply by the derivative of
3x2+2.
So you're left with
3(3x2+2)2×6xNext use the same method for
e(3x):
First differentiate
et which is
et (this is one of the standard derivatives that you'll need to learn).
Then multiply this by the derivative of
3x.
So you get
e3x×3.
There are standard results that are useful to learn e.g. the derivative of
eax is
aeax. But you can derive all these quickly using the chain rule.