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

1 Answer
Jim G.
Feb 10, 2017

#(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)#

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