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

1 Answer

Jul 21, 2016

#d f(x)=[2(4-x^2)(1+x^2)-2x(2x+1)(1+x^2)+2x(2x+1)(4-x^2)] d x#

Explanation:

#y=a*b*c" ; "y^'=a'*b*c+b^'*a.c+c^'*a*b#

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

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

#d f(x)=[2(4-x^2)(1+x^2)-2x(2x+1)(1+x^2)+2x(2x+1)(4-x^2)] d x#

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