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lovesit2x
 2 years ago
Find (d^(2)y)/(dx^(2)) for the following function.
y=e^(4x^(2))
lovesit2x
 2 years ago
Find (d^(2)y)/(dx^(2)) for the following function. y=e^(4x^(2))

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

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

lovesit2x
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]

satellite73
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.1Do you understand how Sat got that first derivative? c:

zepdrix
 2 years 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
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0omg, its that easy??? why am i overthinking this

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

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

zepdrix
 2 years 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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