Question

How do you find the second derivative of `y=e^(pix)`?

Answer 1

`(d^2y)/(dx^2)=pi^2e^(pix)`

Explanation:

To obtain the first derivative use the `color(blue)"chain rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx[e^(f(x))]=e^(f(x)).f'(x))color(white)(2/2)|)))`

`rArrdy/dx=e^(pix).d/dx(pix)=pie^(pix)`

Repeat the process to obtain the second derivative, by differentiating the first derivative.

`rArr(d^2y)/(dx^2)=pie^(pix).d/dx(pix)`

`color(white)(d^2y/dx^2)=pi^2e^(pix)`