anonymous
  • anonymous
help me in finding the derivative of the function below pls y = 7x^3(x^3-3)^5 / (4x+1)^3(7-x^5)^6
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
as there is a division try applying the quotient rule (vdu-udv/v^2) the numbers are very awkward youll probably want to use a calculator, or derive it with that if your calculator can
anonymous
  • anonymous
entering it how you posted it into mine i got -(60x^16+12x^15-1080x^13-225x^12+7560x^10+1620x^9-25920x^7-5670x^6+43740x^4+9720x^3-29160x-6561)/(16807x^28(4x+1)^4)
anonymous
  • anonymous
@Taplin44 i attached a picture of the function so you can understand clearly. pls help me
1 Attachment

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anonymous
  • anonymous
The question asks for dy/dx yes ? if so the verrrry long string of numbers i posted is the correct answer note that 16807x^28(4x+1)^4 is all the denominator to the rest
anonymous
  • anonymous
@Taplin44 how bout this picture? is it clear for you?
1 Attachment
amistre64
  • amistre64
just pull the bottom up and run a 4 term product rule ... abcd \(\color{red}{\to}a'bcd+ab'cd+abc'd+abcd'\)
anonymous
  • anonymous
@amistre64 do i have to use quotient rule, product rule, and chain rule?
amistre64
  • amistre64
id just use the product rule on something this messy
amistre64
  • amistre64
\[y=7x^3~(x^3-3)^5~(4x+1)^{-3}~(7-x^5)^{-6}\]
anonymous
  • anonymous
The picture is clear. It is just alot of arithmetic to do by hand hence why i evaluated with a calculator for you The quotient or product rule will work. Using the product rule requires you to bring up the denominator but as @amistre64 said, is going to be a lot easier
amistre64
  • amistre64
the results will still be a long string tho :) and you would be able to simplify it by factoring out what amounts to the square of the bottom
anonymous
  • anonymous
@taplin44 well our teacher requires us to use the quotient rule, product rule, and chain rule
amistre64
  • amistre64
the quotient rule is pretty well obsolete since dividing is just another way of multiplying. The rule is a throw back to the limit method i believe
amistre64
  • amistre64
you are still applying the product rule, the power rule, and the chain rule in this setup
anonymous
  • anonymous
okaay thank u :)
anonymous
  • anonymous
@Taplin44 @amistre64 how to find the derivative of the numerator? help
amistre64
  • amistre64
the numerator is just a product ... ab \(\to\) a'b + ab'
amistre64
  • amistre64
let a = 7x^3 let b=(x^3-3)^5 define their own prospective derivatives and fill in the rule ....
anonymous
  • anonymous
@amistre64 @Taplin44 how to simplify the attached? help
1 Attachment
anonymous
  • anonymous
@rose21 here!
rose21
  • rose21
yea I see lol
anonymous
  • anonymous
@rose21 attached is the equation. find the derivative. help me
1 Attachment
anonymous
  • anonymous
you have to use logarithemc diffrentation
anonymous
  • anonymous
@Ahmad1 we haven't encountered that topic yet. all i know is to find the derivative by using quotient rule, product rule, and chain rule
anonymous
  • anonymous
trust me I'm telling you the idea for such questions , it's simple by the way \[\ln(y)=3\ln(7x)+5\ln(x^3-3)-3\ln(4x+1)-6\ln(7-x^5)\], now differntiate both sides , the LHD is dy/dx *1/y , so multiply by y to get y prime , i.e\[dy/dx=y*(RHS) \prime\] which is easy to find
anonymous
  • anonymous
im sorry but idk what that is
anonymous
  • anonymous
don't you know the logarithmic function ? I have just used its properties
anonymous
  • anonymous
no sorry. we haven't encountered that yet.
anonymous
  • anonymous
okay no problem ..
anonymous
  • anonymous
@UsArmy3947 here!
anonymous
  • anonymous
@UsArmy3947 find the derivative
1 Attachment
anonymous
  • anonymous
@Ahmad1 how to simplify the attached?
1 Attachment
anonymous
  • anonymous
@rose21 how to simplify the attached?
1 Attachment
UsArmy3947
  • UsArmy3947
ok simplify the attachment on top?
anonymous
  • anonymous
@UsArmy3947 this one
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UsArmy3947
  • UsArmy3947
ok thx
UsArmy3947
  • UsArmy3947
ok i cant help u but ill ask my friend ok?
anonymous
  • anonymous
ok
anonymous
  • anonymous
is this the derivative of the function?
UsArmy3947
  • UsArmy3947
@thomaster @shkrina @robtobey @elisuzsmith @razor99 @terenzreignz @tshark14 @Tron_Cat @YourMentor
anonymous
  • anonymous
@Ashleyisakitty @andriod09 @allie_bear22 @ankit042 @Ashja @ashley_f97
UsArmy3947
  • UsArmy3947
im sorry if i couldn't help u
anonymous
  • anonymous
it's okay :)
amistre64
  • amistre64
its prolly best not to try to "simplify" it; and just to keep it in its "factored" form. at least thats my opinion
anonymous
  • anonymous
@amistre64 u mean that's the final answer?
UsArmy3947
  • UsArmy3947
@amistre64 @Hero @dumbcow @dan815 @dmezzullo @DebbieG @dlapointe25 @Deivyneee @andriod09 @allie_bear22 @ankit042 @Ashleyisakitty @AnElephant @bashirk @iceicebaby
amistre64
  • amistre64
\[y=7x^3~(x^3-3)^5~(4x+1)^{-3}~(7-x^5)^{-6}\] \[y'=\\ ~~~~7(3)x^2~(x^3-3)^5~(4x+1)^{-3}~(7-x^5)^{-6}\\ +35(3)x^5(x^3-3)^4~(4x+1)^{-3}~(7-x^5)^{-6}\\ -21(4)x^3~(x^3-3)^5~(4x+1)^{-4}~(7-x^5)^{-6}\\ +42(5)x^7~(x^3-3)^5~(4x+1)^{-3}~(7-x^5)^{-7}\] then factoring out a : \((4x+1)^{-6}~(7-x^5)^{-12}\) \[y'=[(4x+1)^{-6}~(7-x^5)^{-12}]\\ [~~~~7(3)x^2~(x^3-3)^5~(4x+1)^{3}~(7-x^5)^{6}\\ +35(3)x^5(x^3-3)^4~(4x+1)^{3}~(7-x^5)^{6}\\ -21(4)x^3~(x^3-3)^5~(4x+1)^{2}~(7-x^5)^{6}\\ +42(5)x^7~(x^3-3)^5~(4x+1)^{3}~(7-x^5)^{4}]\]
amistre64
  • amistre64
i spose the squaring of the bottom is a bit much ... we could simply factor out the higest negative degrees instead for a more simplified form
amistre64
  • amistre64
\[y'=[(4x+1)^{-4}~(7-x^5)^{-7}]\\ [~~~~7(3)x^2~(x^3-3)^5~(4x+1)~(7-x^5)\\ +35(3)x^5(x^3-3)^4~(4x+1)~(7-x^5)\\ -21(4)x^3~(x^3-3)^5~~(7-x^5)\\ +42(5)x^7~(x^3-3)^5~(4x+1)]\]
amistre64
  • amistre64
factoring out the smallest exponents of the top gets us: \[y'=[x^2(x^3-3)^4]\\ [~~~~7(3)~(x^3-3)~(4x+1)~(7-x^5)\\ +35(3)x^3~(4x+1)~(7-x^5)\\ -21(4)x~(x^3-3)~~(7-x^5)\\ +42(5)x^5~(x^3-3)~(4x+1)]\\ -----------------\\ ~~~~~~~~~~(4x+1)^{4}~(7-x^5)^{7}\] and theres some constants we could pull as well

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