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Quotient rule

Hello i'm finding the following question difficult could someone explain to me how to answer this by using the quotient rule, thank you :smile:.

y= 2sin5x/x3
Original post by Mr. Study
Hello i'm finding the following question difficult could someone explain to me how to answer this by using the quotient rule, thank you :smile:.

y= 2sin5x/x3


Is that y=2sin⁡5xx3\displaystyle y=\frac{2 \sin 5x}{x^3} ?

If so let u=2sin⁡5xu=2 \sin 5x and v=x3v=x^3.

Differentiate both and bung it into your formula.
Original post by Mr. Study
Hello i'm finding the following question difficult could someone explain to me how to answer this by using the quotient rule, thank you :smile:.

y= 2sin5x/x3


U = 2sin5x, V=x³ and just use the standard quotient rule formula

Posted from TSR Mobile
Original post by Mr. Study
Hello i'm finding the following question difficult could someone explain to me how to answer this by using the quotient rule, thank you :smile:.

y= 2sin5x/x3


You can let u=2sin5v, and v=x3

Then differentiate both of the above, and substitute what you have got into the quotient rule formula.
Original post by Mr. Study
Hello i'm finding the following question difficult could someone explain to me how to answer this by using the quotient rule, thank you :smile:.

y= 2sin5x/x3


u = 2sin5x ----------v = x3
u' = 10cos5x---------------- v' = 3x2

y' = (vu'-uv')/v2
= 10x3cos5x + 6x2sin5x

I think :redface:
(edited 10 years ago)
Reply 5
Avatar for Old_Simon
Old_Simon
12
The quotient rule is completely unnecessary and just one more thing to remember.
(edited 10 years ago)
Original post by Old_Simon
The quotient rule is completely unnecessary and just one more thing to remember.


This particular example is crying out for product rule.
Reply 7
Avatar for TenOfThem
TenOfThem
18
Original post by StarvingAutist
u = 2sin5x v = x-3
u' = 10cos5x v' = -3x-4

y' = (vu'-uv')/v2
= 10x-3cos5x + 6x-4sin5x

I think :redface:


This does not actually make sense

You seem to be quoting the quotient rule and using the product rule
Original post by TenOfThem
This does not actually make sense

You seem to be quoting the quotient rule and using the product rule


changed it lol, I realised... :I
Reply 9
Avatar for TenOfThem
TenOfThem
18
Original post by Old_Simon
The quotient rule is completely unnecessary and just one more thing to remember.


No, it is one more thing to be intelligently derived from something that you know

It simplifies the outcome of the product rule rather nicely without having to worry about adding the fractions
It would be a lot easier to use the product rule with 2sin(5x) and x-³.

Posted from TSR Mobile
Original post by majmuh24
It would be a lot easier to use the product rule with 2sin(5x) and x-³.

Posted from TSR Mobile


Yup. It would :wink:
Original post by Mr M
This particular example is crying out for product rule.


Indeed it is :wink:

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