How do you differentiate # f(x)=(2x+1)(4-x^2)(1+x^2) # using the product rule?

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Answer 1 · 2016-10-12T06:34:35

#10x^4+4x^3-18x^2-6x-8#

You could further simply it if you are required to do so.

Multiply #(1+x^2)# by #(4-x^2)#: #(4+3x^2-x^4)#

#((2x+1)'(4+3x^2-x^4))+((2x+1)(4+3x^2-x^4)')#

#(2(4+3x^2-x^4))+((2x+1)(6x-4x^3))#

#(8+6x^2-2x^4)+(6x+12x^2-4x^3-8x^4)#

#8+6x^2-2x^4+6x+12x^2-4x^3-8x^4#

#8+6x+18x^2-4x^3-10x^4#

Optional, divide by #-1#,

#10x^4+4x^3-18x^2-6x-8#

Good Luck