What are the critical points of #f(x) =2e^(3x)-3xe^(2x)#?
To compute critical points of a function, you need its first derivative.
We need two rules: first of all, the derivative doesn't care about multiplicative factors, so
The chain rule states that
Which in your case becomes
So, the whole derivative is
In addition to what we saw before, we need to add the rule for deriving a product of two functions, which is
So, we have that
Finally, sum up the two pieces: we have
And we can factor