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

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abb0tBest ResponseYou've already chosen the best response.0
So find the second derivative of the function.
 one year ago

abb0tBest ResponseYou've already chosen the best response.0
This requires that you use the chain rule.
 one year ago

lovesit2xBest ResponseYou've already chosen the best response.0
\[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{4x ^{2}}\]
 one year ago

abb0tBest ResponseYou've already chosen the best response.0
First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.
 one year ago

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

satellite73Best ResponseYou've already chosen the best response.1
first derivative is \[8xe^{4x^2}\] by the chain rule second derivative requires the product rule
 one year ago

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

zepdrixBest 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! :)
 one year ago

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

zepdrixBest 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!
 one year ago

lovesit2xBest ResponseYou've already chosen the best response.0
omg, its that easy??? why am i overthinking this
 one year ago

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

lovesit2xBest ResponseYou've already chosen the best response.0
n the second is the 8x e ^4x^2
 one year ago

zepdrixBest 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!
 one year ago
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