How do you differentiate #f(x) =(2+x )( 2-3x)# using the product rule?

2 Answers
Jun 7, 2017

Answer:

#-6x -4#

Explanation:

#f(x) = (2 + x)(2 - 3x)#

let say #u = (2 + x)#, then #u' = 1# and #v =(2 - 3x)#, then #v' = -3#

#f'(x) = uv' + vu'#

#f'(x) = (2 + x)(-3) +(2 - 3x)(1)#

#f'(x) = -6 -3x +2 - 3x = -6x -4#

Jun 7, 2017

Answer:

-6x-4

Explanation:

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#.