Question

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

Answer 1

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

Explanation:

differentiate using the `color(blue)"chain rule"`

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

`"the first derivative is"`

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

`"The second derivarive is the derivative of " dy/dx`

`"Repeat the process using the chain rule"`

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