Here's the question you clicked on:
lovesit2x
Find (d^(2)y)/(dx^(2)) for the following function. y=e^(-4x^(2))
So find the second derivative of the function.
This requires that you use the chain rule.
\[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{-4x ^{2}}\]
First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.
You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]
first derivative is \[-8xe^{-4x^2}\] by the chain rule second derivative requires the product rule
Do you understand how Sat got that first derivative? c:
\[\large y'=-8xe^{-4x^2}\] So now you need to find the second derivative as was stated above. \(\large y''\) To differentiate this a second time, you'll need to apply the Product Rule, very similarly to the way we did it in the last problem! :)
Fine fine fine D: I'll do the pretty colors like last time. Maybe that will help.
\[\huge y''=\color{royalblue}{\left(-8x\right)'}e^{-4x^2}-8x\color{royalblue}{\left(e^{-4x^2}\right)'}\]Product Rule setup for the second derivative. The second blue term should give you the same thing you got for the first derivative!
omg, its that easy??? why am i overthinking this
What do you get for the first set of blue brackets?
n the second is the -8x e ^-4x^2
\[\huge y''=\color{orangered}{\left(-8\right)}e^{-4x^2}-8x\color{orangered}{\left(-8xe^{-4x^2}\right)}\] Like that? Yay good job!