Answer
$$y''=2e^{x^2}(1+2x^2)$$
Work Step by Step
$$y=e^{x^2}+5x$$
- Find $y'$: $$y'=e^{x^2}(x^2)'+5=2xe^{x^2}+5$$
- Find $y''$: $$y''=2(xe^{x^2})'+(5)'=2\Big((x)'e^{x^2}+x(e^{x^2})'\Big)+0$$ $$y''=2\Big(e^{x^2}+xe^{x^2}(x^2)'\Big)=2\Big(e^{x^2}+2x^2e^{x^2}\Big)$$ $$y''=2e^{x^2}(1+2x^2)$$