Question

Help
8. Find the first derivative of \( y=\left(2 x^{2}+1\right)\left(x^{3}+4 x+3\right) \)

Answer 1

Hi,

Explanation:

Method 1: we develop

`f(x)=(2x^2+1)(x^3+4x+3)\\=2x^5+8x^3+6x^2+x^3+4x+3\\=2x^5+9x^3+6x^2+4x+3\\\\f'(x)=10x^4+27x^2+12x+4\\\\`

Method 2: (uv)'=u'v+uv'

`f(x)=(2x^2+1)(x^3+4x+3)\\f'(x)=4x(x^3+4x+3)+(2x^2+1)(3x^2+4)\\=4x^4+16x^2+12x+6x^4+8x^2+3x^2+4\\\\=10x^4+27x^2+12x+4\\`