How do you differentiate #f(x)=x^3(4x - 12)# using the product rule?

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Answer 1 · 2015-12-14T05:41:24

Product Rule:
If we have two functions #f(x)# and #g(x)#, then
#d/dx# #f(x)g(x)# = #f^'(x)g(x) + f(x)g^'(x)#

Original Equation:
#f(x)=x^3(4x-12)#

The two equations you're multiplying are #x^3# and #(4x-12)#

Take the derivative of the first equation (#x^3#) and times it by the second equation (#(4x-12)#)

You should get #(3x^2)•(4x-12)#

Next, take the derivative of the second equation (#(4x-12)#) and times it by the first (#x^3#).

You should get #(x^3)•(4)#

Now add them together.

You should get #((3x^2)•(4x-12) )+ ((x^3)•(4))#

Multiply it out and combine like terms.

Your final answer should be #16x^3-36x^2#