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

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Answer 1 · 2015-10-05T19:59:14

#(df(x))/dx=-10x^4-4x^3+18x^2+6x+8#

#f(x)=(8x+4-2x^3-x^2)(1+x^2)#
#f(x)=8x+8x^3+4+4x^2-2x^3-2x^5-x^2-x^4#
#f(x)=-2x^5-x^4+6x^3+3x^2+8x+4#

#(df(x))/dx=-10x^4-4x^3+18x^2+6x+8#

Answer 2 · 2015-10-05T20:05:06

The product rule for 3 factors is: #d/dx(uvw) = u'vw+uv'w+uvw'#

So

#f'(x) = (2)(4-x^2)(1+x^2)+ (2x+1)(2x)(1+x^2) +(2x+1)(4-x^2)(2x)#

Simplify algebraically as you see fit.