Question

!!!!!

If f(x) = −2x^5−3x^4−6x^3 / x4, find f′(x)

Answer 1

I keep getting -10x^4 - 12X^3 - 18x^2 / 4x^3 ....but it's wrong

Answer 2

I also tried simplifying that, but it didnt work

Answer 3

What rule do the ratios require?

Answer 4

i'm not sure what you mean

Answer 5

I guess i'm missing a big component

Answer 6

Does quotient rule ring a bell?

Answer 7

You could also try simplifying the original function then take the derivative or bring it up and use product rule, there's plenty of things you can do with this.

Answer 8

I simplified and brought it up to -5x^4-4x^3-9x^2

Answer 9

I do remember the quotient rule!

Answer 10

but I dont get why the simplified answer didnt work

Answer 11

that's not the answer.

Answer 12

oops should read \[f(x) = -2x - 3 - \frac{18}{4} x^{-2}\]

Answer 13

that is the simplified function... now find the 1st derivative

Answer 14

Ah that looks much better, the derivative should be very easy from here :p

Answer 15

It just requires the power rule nothing to fancy

Answer 16

would I multiply 18/4 by -2? sorry, i'm very new to this

Answer 17

\[\frac{ d }{ dx }x^n = nx^{n-1}\]

Answer 18

mr. batman!!

Answer 19

When I use that power rule, the first value (-2x) becomes (-2)

Answer 20

Yes

Answer 21

I don't know how to tackle the last value of (18/4) x^ -2 ..... I want to multiple 18/4 by 2 and be left with x^(-2-1 = 3)

Answer 22

-2 - 3 -18/4 x^-2
-5 - ( -2 * 18/4) x^-3

Answer 23

(-5) - (-9)x^-3

Answer 24

(-5) + 9x^-3

Answer 25

I don't know where I went wrong with the power rule

Answer 26

the 1st term is -3x so

\[f'(x) = -3 +\frac{9}{x^3}\]

Answer 27

that's not the answer though...or are you just showing the next step? i'm going to try using the quotient rule...so confused

Answer 28

what answer do you have..?

Answer 29

they don't tell you the answer online, until you get it correct...that's the only way of knowing or waiting until the deadline is over....ill try the quotient rule and see if that works

Answer 30

you get unlimited chances to guess correct, luckily

Answer 31

well here it is

\[f(x) = -2x - 3 - \frac{18}{4} x^{-2}\]

then

\[f'(x) = -2 + \frac{9}{x^3}\]

Answer 32

I typed that in .. and it was wrong

Answer 33

hmmm maybe there was a mistake in simplifying

Answer 34

f(x)= (−2x^5)−(3x^4) − (6x^3) / x4 find f′(x).

Answer 35

@campbell_st @iambatman

Answer 36

hey is that all over x^4
or is just the last term over x^4?

Answer 37

\[f(x)=-2x^5-3x^4-\frac{6x^3}{x^4} \text{ or } f(x)=\frac{-2x^5-3x^4-6x^3}{x^4}\]

Answer 38

and yes it seems something went wrong with the simplification above

Answer 39

\[f(x)=-2x^{5-4}-3x^{4-4}-6x^{3-4}\]
I think it was just the last term that might have been written incorrectly

Answer 40

try to simplify that
yourself
and then find the derivative

Answer 41

if you want i can check your work

Answer 42

yes please!!!! ive been on this question for the last 1 hour!!! im going to check what you did right now

Answer 43

it's all over x^4

Answer 44

I used the quotient rule and got -2x^8 + 6x^6 / x^8 ...and it was wrong!

Answer 45

well do you understand my rewriting of f(x)?

Answer 46

\[f(x)=-2x^{5-4}-3x^{4-4}-6x^{3-4} \]

Answer 47

not really, I dont understand that 4-4 or the 3-4

Answer 48

we don't need quotient rule
just power rule and constant rule

Answer 49

i did top exponent - bottom exponent

Answer 50

yeah ...can I do it like this:

Answer 51

-10x^4 - 12x^3 -18x^2 / 4x^3

Answer 52

what did you do to get that?

Answer 53

I brought the 5 down and multiplied it by the -2...

Answer 54

then took one away from the x and got -10x^4

Answer 55

ok i don't know what you did and it doesn't look good and not trying to be mean when i say that
but I think you want to look at this the easiest way possible

Answer 56

\[f(x)=\frac{-2x^5-3x^4-6x^3}{x^4}=\frac{-2x^5}{x^4}-\frac{3x^4}{x^4}-\frac{6x^3}{x^4}\]
wrote as 3 separate fractions

Answer 57

I was trying to use the quotient rule...but if there's an easier way, that's better

Answer 58

oh i see where you're talking about

Answer 59

\[f(x)=-2x-3-\frac{6}{x}\]
do you understand this

Answer 60

x^0 is one

Answer 61

that's why it's 3, right?

Answer 62

\[f(x)=-2x-3-6x^{-1} \]

Answer 63

yes

Answer 64

try to differentiate that

Answer 65

show me what you get

Answer 66

ok let me see

Answer 67

i will do quotient rule for you after this
and show you is lot uglier

Answer 68

6/x^2 - 2

Answer 69

guess what?! :)

Answer 70

it looks good

Answer 71

it took me long to get to that!...how would you differentiate it in an easier way?

Answer 72

the answer worked!!!!!!!!

Answer 73

no that is the easy way

Answer 74

you're awesome!

Answer 75

\[f'(x)=\frac{(-2x^5-3x^4-6x^3)'(x^4)-(x^4)'(-2x^5-3x^4-6x^3)}{(x^4)^2}\]
this is the quotient rule setup

Answer 76

yes, that's exactly what I tried out!

Answer 77

one sec my cat is an obstacle i have to work around to type of keyboard
be patient with me
sorry

Answer 78

it's okay!!! im patient...I wont go anywhere till I know how to do quotient rule for this question...i tried so many times

Answer 79

\[f'(x)=\frac{(-10x^4-12x^3-18x^2)x^4-4x^3(-2x^5-3x^4-6x^3)}{x^8} \\ \frac{-10x^8-12x^7-18x^6+8x^8+12x^7+24x^6}{x^8} \\ \frac{-2x^8+0x^7+6x^6}{x^8} \\ \frac{-2x^8}{x^8}+\frac{0x^7}{x^8}+\frac{6x^6}{x^8} \\ -2+0+\frac{6}{x^2}\]

Answer 80

tons uglier but still works

Answer 81

you still have to separate the fractions to simplify

Answer 82

I dont get how you got 0x^7

Answer 83

-12x^7+12x^7

Answer 84

-12+12=0

Answer 85

-12x^7 + 12x^7 should just cancel out

Answer 86

yes

Answer 87

thankyou so much!!!! I guess it was just the last step i messed up on!

Answer 88

needed to simplify the bottom exponent as well!!!!

Answer 89

(-12+12)x^7
0x^7
0 <---or yeah this means you can just cancel them out

Answer 90

thank-you so much!!! where are you from?!! and are you a TA for a university?

Answer 91

i retired from teaching a few months ago
i'm from southern US

Answer 92

okay, that makes sense. you explain everything very well

Answer 93

I'm horrible at typing
Sometimes my sentences come out sorta bad

Answer 94

nope, I understood everything! you were so patient with me too! I really appreciate it

Answer 95

np
Good luck on the rest of your work @sharmit
I must log off for tonight

Answer 96

thankyou so much! sweet dreams!