Mathematics
OpenStudy (anonymous):

et f(x) = x^4 e^(-6 x) Find a formula for the first and second derivatives of f. f'(x) = eAx (Bx4 + Cx3) and f''(x) = eDx (Ex4 + Fx3 + Gx2) where i think they want me to find A.B.C.D.E.F.G

myininaya (myininaya):

Do you know how to find the first derivative?

myininaya (myininaya):

$f(x)=x^4 \cdot e^{-6x} \text{ use product rule please}$ $f'(x)=(x^4)' \cdot e^{-6x}+x^4 \cdot (e^{-6x})'$

myininaya (myininaya):

I wait to hear what you think is the next step...

OpenStudy (anonymous):

sorry i was trying the problem

OpenStudy (anonymous):

u use the product rule to find the second derivative?

OpenStudy (anonymous):

for the first derivative dont u factor out like terms?

myininaya (myininaya):

$f'(x)=4x^3 e^{-6x}+x^4(-6)e^{-6x}=x^3e^{-6x}(4-6x)$ $f''(x)=(x^3)' \cdot e^{-6x}(4-6x)+x^3 \cdot (e^{-6x})' \cdot (4-6x)+x^3e^{-6x} \cdot (4-6x)'$ $f''(x)=3x^2 \cdot e^{-6x}(4-6x)+x^3 \cdot (-6)e^{-6x} \cdot (4-6x)+x^3e^{-6x}(0-6)$ $f''(x)=e^{-6x}(3x^2(4-6x)+x^3(-6)(4-6x)+x^3(-6))$ Now it is just a little bit of algebra to put it in the form they want to determine the coefficients.

OpenStudy (anonymous):

wait so for the first derivative i got e^-6x(5x^4+4x^3)

myininaya (myininaya):

yes i did a little renaming if you didn't notice

OpenStudy (anonymous):

oh lol

OpenStudy (anonymous):

so A=-6 b= 5 c= 4

myininaya (myininaya):

That first line is f' Second line is f'' Third line is f'' fourth line is f''

myininaya (myininaya):

$C=4, B=-6 ,A=-6$ hmmmm how did you get B=5? you have e^{-6x} right not e^{5x}

myininaya (myininaya):

So your B is the only thing I don't agree with

OpenStudy (anonymous):

ok so for the second derivative i got

OpenStudy (anonymous):

d=-6, e=5,f=4,g=3

OpenStudy (anonymous):

wait g= 4

OpenStudy (anonymous):

e =3

myininaya (myininaya):

E,F,G I see something totally different

OpenStudy (anonymous):

im adding the like terms together, am i doing it correctly?

myininaya (myininaya):

$f ''(x)=e^{-6x}(3x^2(4-6x)+x^3(-6)(4-6x)+x^3(-6))$ $f''(x)=e^{-6x}(x^4(-6)(-6)+x^3(-18-24-6)+x^2(3(4)))$

myininaya (myininaya):

Yes put all your like terms together after factoring out e^{-6x}

OpenStudy (anonymous):

Ok so e=36 , f=-48, g=12

OpenStudy (anonymous):

am i right?

myininaya (myininaya):

OpenStudy (anonymous):

yeah

OpenStudy (anonymous):

your'e better than my math teacher! lol

OpenStudy (anonymous):

u should actually be my math professor ! lol

myininaya (myininaya):

That is sweet! Thanks.