Question

How do you find the derivative for `f(x) = (2x+1)(4-x^2)(1+x^2)`?

Answer 1

`y'=2(-5x^4-2x^3+9x^2-3x+4)`.

Explanation:

in this way:

`y'=2*(4-x^2)(1+x^2)+(2x+1)* (-2x)*(1+x^2)+(2x+1)(4-x^2)*2x=`

`=2(4+4x^2-x^2-x^4-2x^2-2x^4-x-x^3+8x^2-2x^4+4x-x^3)=`

`=2(-5x^4-2x^3+9x^2-3x+4)`.