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

Answer 1

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

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)#

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Answer 2

Axel Alvarez

To find the second derivative of ( y = e^{-\pi x} ), you need to take the derivative twice.

The first derivative is ( y' = -\pi e^{-\pi x} ).

Taking the derivative of ( y' ), we get the second derivative:

( y'' = (-\pi)(- \pi e^{-\pi x}) = \pi^2 e^{-\pi x} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.