Question

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

Answer 1

Do you know how to find the first derivative?

Answer 2

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

Answer 3

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

Answer 4

sorry i was trying the problem

Answer 5

u use the product rule to find the second derivative?

Answer 6

for the first derivative dont u factor out like terms?

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

oh lol

Answer 11

so A=-6 b= 5 c= 4

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

ok so for the second derivative i got

Answer 16

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

Answer 17

wait g= 4

Answer 18

e =3

Answer 19

E,F,G I see something totally different

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

am i right?

Answer 25

i agree with your answers

Answer 26

yeah

Answer 27

your'e better than my math teacher! lol

Answer 28

u should actually be my math professor ! lol

Answer 29

That is sweet! Thanks.