Question

find the derivative of the function.
g(t)=e (to the power of-3/t^2)

Answer 1

Exponentials of base e are always nice to work with :)
Since we know the derivative of e^x = e^x...
(d/dx) e^(something messy) = e^(something messy) * (d/dx)(something messy)
Understand? :o

Answer 2

well kinda. i was getting help from this other person and he or she told me to find the derivative of -3/t^2 and then multiply it by e^-3/t^2? right?

Answer 3

\[\frac{d}{dx}e^{\text{something}}=\frac{d}{dx}\text{something}\times e^{\text{something}}\]

Answer 4

so this is what i have g prime(t)=0 times t-2 +-2t(-3) is this correct?

Answer 5

\[\frac{d}{dt}\frac{-3}{t^2}=6t^{-3}=\frac{6}{t^3}\]

Answer 6

by the power rule right?
\[\frac{-3}{t^2}=-3t^{-2}\] so the derivative is
\[-2\times -3t^{-2-1}=6t^{-3}=\frac{6}{t^3}\]

Answer 7

i think i need to start all over again sorry :[

Answer 8

lol @zepdrix wrote the exact same thing i did, before i did!

Answer 9

hahaha

Answer 10

written in math, the derivative of \(e^{f(t)}\) is \(f'(t)e^{f(t)}\)

Answer 11

@satellite73 Hey sometimes I see people writing stuff in equation form, but in very large text, how do you do that? :C

Answer 12

\large

Answer 13

help me?

Answer 14

if you ever want to see code, right click and select "show math" as then "latex"

Answer 15

oh sorry lil XD didn't mean to hijack your post lol

Answer 16

thanks guys :[

Answer 17

\[\huge e^x\]

Answer 18

lotta help ;{{{{{{{{{{

Answer 19

ok here we have
\[e^{f(t)}\] with \(f(t)=-\frac{3}{t^2}, f'(t)=\frac{6}{t^3}\) right?

Answer 20

or is this still confusing?

Answer 21

still confusing......im sorry im so HARD to work with

Answer 22

no problem
but we still have the power rule we can use yes?

Answer 23

yup

Answer 24

so our real job is to find the derivative of \(-\frac{3}{t^2}\) right? i mean that is really all we need to do

Answer 25

okay

Answer 26

once we have that, we are done

Answer 27

alright

Answer 28

so how do you write \(-\frac{3}{t^2}\) in exponential notation (in one line, rather than as a fraction?)

Answer 29

ummm -3(t^-2)

Answer 30

yes. now apply the all mighty power rule

Answer 31

okay... so we dont use the product rule at all?

Answer 32

oh NO
now when you have a constant like \(-3\) or any other constant for that matter

Answer 33

*not

Answer 34

for example, the derivative of \(\sin(x)\) is \(\cos(x)\) so the derivative of \(7\sin(x)\) is \(7\cos(x)\)

Answer 35

o okay

Answer 36

soapplying the power rule to -3(t^-2) its -3(-2t)?

Answer 37

what is \(-2-1\) ?

Answer 38

-3

Answer 39

yes, so that is your exponent from the power rule
subtract one from the exponent of \(-2\) to get \(-2-1=-3\)

Answer 40

\[\frac{d}{dx}x^n=nx^{n-1}\] whether \(n\) is positive, negative, a fraction, or even an irrational number

Answer 41

okay so then putting this all together my answer to this question is 6t^-3 *e^-3/t^2? right?

Answer 42

yes that is the whole story
although you might want to write it as
\[\frac{6}{t^3}e^{-\frac{3}{t^2}}\]

Answer 43

okay gotcha thanks SOOOO much for ur help i APPRECIATE IT SO MUCH!

Answer 44

or not, as the case may be
but generally it is helpful not to have negative exponents, especially if you need further computation
yw

Answer 45

invoice is in the mail

Answer 46

?

Answer 47

just kidding

Answer 48

ok
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