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 $-1$ ,

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

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