How do you find the second derivative of $y = e^{π x}$ $y=e^(pix)$ ?

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How do you find the second derivative of $y = e^{π x}$ $y=e^(pix)$ ?

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Answer 1 · 2017-02-10T19:19:45

$\frac{d^{2} y}{{d x}^{2}} = π^{2} e^{π x}$ $(d^2y)/(dx^2)=pi^2e^(pix)$

Explanation:

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

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

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

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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How do you find the second derivative of $y = e^{π x}$ $y=e^(pix)$ ?

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Explanation:

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