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abb0t
 one year ago
Best ResponseYou've already chosen the best response.0So find the second derivative of the function.

abb0t
 one year ago
Best ResponseYou've already chosen the best response.0This requires that you use the chain rule.

lovesit2x
 one year ago
Best ResponseYou've already chosen the best response.0\[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{4x ^{2}}\]

abb0t
 one year ago
Best ResponseYou've already chosen the best response.0First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.

Xavier
 one year ago
Best ResponseYou've already chosen the best response.0You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]

satellite73
 one year ago
Best ResponseYou've already chosen the best response.1first derivative is \[8xe^{4x^2}\] by the chain rule second derivative requires the product rule

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Do you understand how Sat got that first derivative? c:

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large y'=8xe^{4x^2}\] 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! :)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Fine fine fine D: I'll do the pretty colors like last time. Maybe that will help.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge y''=\color{royalblue}{\left(8x\right)'}e^{4x^2}8x\color{royalblue}{\left(e^{4x^2}\right)'}\]Product Rule setup for the second derivative. The second blue term should give you the same thing you got for the first derivative!

lovesit2x
 one year ago
Best ResponseYou've already chosen the best response.0omg, its that easy??? why am i overthinking this

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1What do you get for the first set of blue brackets?

lovesit2x
 one year ago
Best ResponseYou've already chosen the best response.0n the second is the 8x e ^4x^2

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\huge y''=\color{orangered}{\left(8\right)}e^{4x^2}8x\color{orangered}{\left(8xe^{4x^2}\right)}\] Like that? Yay good job!
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