Question

f(x)=(e)^(-4x^(2))
need f of 1 and f of 2.

Answer 1

just plgu in 1 for x and 2 for x

Answer 2

f(x)=(e)^(-4x^(2))
f(1)=(e)^(-4(1)^(2))
f(2)=(e)^(-4(2)^(2))

Answer 3

i meant f'(x) and f"(x)

Answer 4

my bad

Answer 5

lol f(x) means f of x lol
umm use the produce rule again...we already showed you in a different problem

Answer 6

i know. i keep getting the wrong answers though. i suck at this.

Answer 7

actually you don't use the product rule because its e^

Answer 8

and how would i use the product rule theres only an e raised to something

Answer 9

you know how to find the derivative of e^x?

Answer 10

its e^x

Answer 11

f(x)=e^x
f'(x)=e^x * x'

Answer 12

replace the x with all that messy stuff and find derivative

Answer 13

why isnt the f'(x) = to -4e^-4x^2

Answer 14

brb

Answer 15

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

f'(x)=(e)^(-4x^(2)) * (-4x^(2))'
f'(x)=(e)^(-4x^(2)) * (2*-4x^(2-1))
f'(x)=(e)^(-4x^(2)) * (-8x^(1))
f'(x)=(e)^(-4x^(2)) * (-8x)

Answer 16

for f''(x) you use the product rule

Answer 17

can u please show what the answer is? im having trouble with these

Answer 18

the e is what is messing me up mainly... also all the powers

Answer 19

We have
\[f(x)=e^{-4x^2}\]
Let's find f'(x)
\[f'(x)= \frac{d}{dx} e^{-4x^2}\]
we get
\[f'(x)= e^{-4x^2}\frac{d}{dx} (-4x^2)\]
so we get
\[f'(x)= e^{-4x^2}(-8x)\]

Answer 20

understood

Answer 21

Now let's find f''(x) or second derivative of x
\[f''(x)=\frac{d}{dx}( e^{-4x^2}(-8x))\]
We'll use product rule here
\[(fg)'=f'g+g'f\]
so we get here
\[f''(x)=(-8x)\frac{d}{dx} (e^{-4x^2}) +e^{-4x^2}\frac{d}{dx} (-8x)\]
we get now
\[f''(x)=(-8x)(e^{-4x^2}\frac{d}{dx}(-4x^2) ) +e^{-4x^2}(-8)\]
so we get
\[f''(x)=(-8x)(e^{-4x^2}(-8x) ) +e^{-4x^2}(-8)\]
let's simplify now
\[f''(x)=(-8x)\times (-8x)e^{-4x^2} -8e^{-4x^2}\]
we get finally
\[f''(x)=64x^2e^{-4x^2} -8e^{-4x^2}\]

Answer 22

@mariomintchev Did you understand?

Answer 23

im soaking it all in right now. im gonna write it all out on paper.

Answer 24

Yeah , call me if you need help:D

Answer 25

sure thing

Answer 26

so the derivative of e raised to some power is that and the derivative of the power?

Answer 27

yeah
\[\frac{d}{dx} e^x= e^x \time \frac{d}{dx} x\]

Answer 28

sorry
\[\frac{d}{dx} e^x=e^x \times \frac{d}{dx} (x)\]

Answer 29

you're fine. i understood.

Answer 30

Great :D

Answer 31

how would i enter this into a hw site...
it keeps telling me that im making a syntax error

Answer 32

the answer to f"(x)

Answer 33

Maybe like
f''(x)=64x^(2)e^(-4x^(2))-8e^(-4x^2)
or
e^(-4x^(2))(64x^(2)-8)

Answer 34

ok thanks! :D