How do you find the derivative of #Y= x^2 ( 2x + 3 )#?
Method 1 Use the product ruel then simplify.
The product rule tells us that the derivative of a product of two function (I think of them as the First and the Second) is given by:
(Because both addition and multiplication of functions are commutative, other orders are possible.)
So we get (including detail you might prefer to leave out eventually)
(usually we'll omit writing this step, but we need to DO this)
# = 4x^2+6x+2x^2#
# = 6x^2 +6x#
Method 2 Multiply first, the differentiate.
Now we do not need the product rule, just the sum and power and constant multiple ruel)
We can use either method to get to the correct answer. (There are many paths to one destination.)
We can take control of how a problem is written. (Unless our tester has told us we must use a particular method -- that is sometimes done to test our knowledge of that method.)