How do you differentiate #p(y) = y^2sin^2(y)cos(y)# using the product rule?
Consider two of the three functions forming p(y) as a single function, and then use the product rule a second time when calculating its derivative.
The product rule states that
Additionally, let's let
We now have
Applying the product rule gives us
But to calculate
Then, substituting for
Putting it all together gives us