Question

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

Answer 1

`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`