If we want to differentiate #f(x)=(2+x)(2-3x)# using the product rule we use the following #(f')(g)+(g')(f)#. Where #f# is your first term #(2+x)# and #g# is your second term #(2-3x)#. So, we take the #d/dx# of #f# which is 1 using the power rule #nx^(n-1)# keep in mind that the #d/dx# of a constant is zero, while #g# remains the same. At this point what we have is #1(2-3x)# now we take the #d/dx# of #g# which is #-3#, #f# remains the same.

After we have derived the equation we now have the following:

#1(2-3x)-3(2+x)#

Go ahead distribute and simplify:

#2-3x-6-3x=-6x-4#

Our final answer is #-6x-4#.