Question

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

Answer 1

`12x^2+4`

Explanation:

differentiate each term using the `color(blue)"power rule"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))`

`"let " f(x)=x^4+2x^2+3`

`rArrf'(x)=4x^3+4x+0=4x^3+4x`

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

`rArrf''(x)=12x^2+4`