How do you find the second derivative of x^4+2x^2+3?

Jan 10, 2017

$12 {x}^{2} + 4$

Explanation:

differentiate each term using the $\textcolor{b l u e}{\text{power rule}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{let } f \left(x\right) = {x}^{4} + 2 {x}^{2} + 3$

$\Rightarrow f ' \left(x\right) = 4 {x}^{3} + 4 x + 0 = 4 {x}^{3} + 4 x$

To obtain the second derivative, differentiate f'(x) ,again using the power rule.

$\Rightarrow f ' ' \left(x\right) = 12 {x}^{2} + 4$