Question

Find (d^(2)y)/(dx^(2)) for the following function.

y=e^(-4x^(2))

Answer 1

So find the second derivative of the function.

Answer 2

This requires that you use the chain rule.

Answer 3

\[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{-4x ^{2}}\]

Answer 4

First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.

Answer 5

You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]

Answer 6

first derivative is
\[-8xe^{-4x^2}\] by the chain rule
second derivative requires the product rule

Answer 7

Do you understand how Sat got that first derivative? c:

Answer 8

Yes. I do.

Answer 9

yes

Answer 10

\[\large y'=-8xe^{-4x^2}\]

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! :)

Answer 11

Fine fine fine D: I'll do the pretty colors like last time. Maybe that will help.

Answer 12

lol

Answer 13

\[\huge y''=\color{royalblue}{\left(-8x\right)'}e^{-4x^2}-8x\color{royalblue}{\left(e^{-4x^2}\right)'}\]Product Rule setup for the second derivative.
The second blue term should give you the same thing you got for the first derivative!

Answer 14

omg, its that easy???
why am i overthinking this

Answer 15

:3

Answer 16

What do you get for the first set of blue brackets?

Answer 17

-8

Answer 18

n the second is the -8x e ^-4x^2

Answer 19

\[\huge y''=\color{orangered}{\left(-8\right)}e^{-4x^2}-8x\color{orangered}{\left(-8xe^{-4x^2}\right)}\]

Like that?
Yay good job!

Answer 20

i love that lol