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

1. abb0t

So find the second derivative of the function.

2. abb0t

This requires that you use the chain rule.

3. lovesit2x

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

4. abb0t

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

5. Xavier

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

6. satellite73

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

7. zepdrix

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

8. abb0t

Yes. I do.

9. lovesit2x

yes

10. zepdrix

$\large y'=-8xe^{-4x^2}$ 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! :)

11. zepdrix

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

12. lovesit2x

lol

13. zepdrix

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

14. lovesit2x

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

15. zepdrix

:3

16. zepdrix

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

17. lovesit2x

-8

18. lovesit2x

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

19. zepdrix

$\huge y''=\color{orangered}{\left(-8\right)}e^{-4x^2}-8x\color{orangered}{\left(-8xe^{-4x^2}\right)}$ Like that? Yay good job!

20. lovesit2x

i love that lol