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

Jun 14, 2015

$y ' = 2 \left(- 5 {x}^{4} - 2 {x}^{3} + 9 {x}^{2} - 3 x + 4\right)$.

#### Explanation:

in this way:

$y ' = 2 \cdot \left(4 - {x}^{2}\right) \left(1 + {x}^{2}\right) + \left(2 x + 1\right) \cdot \left(- 2 x\right) \cdot \left(1 + {x}^{2}\right) + \left(2 x + 1\right) \left(4 - {x}^{2}\right) \cdot 2 x =$

$= 2 \left(4 + 4 {x}^{2} - {x}^{2} - {x}^{4} - 2 {x}^{2} - 2 {x}^{4} - x - {x}^{3} + 8 {x}^{2} - 2 {x}^{4} + 4 x - {x}^{3}\right) =$

$= 2 \left(- 5 {x}^{4} - 2 {x}^{3} + 9 {x}^{2} - 3 x + 4\right)$.