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Given that y = (4x +1)^3 sin2x find dy/dx

I get that to differentiate it's 12(4x+1)^2 2cos2x

but why does the answer sheet say m=2 and n=12?
Original post by Hirsty97
I get that to differentiate it's 12(4x+1)^2 2cos2x

but why does the answer sheet say m=2 and n=12?


Show the question... like the picture of it then we might be able to find out.
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Avatar for Hirsty97
Hirsty97
OP
21
image-dab21d36-7bfc-410a-a9ac-10b975fd079c2003112198-compressed.jpg.jpeg

image-c7ceb54f-e7ca-4039-8efc-e3d82511dee92034104810-compressed.jpg.jpeg
Try taking log and then diffrenciating both sides. I did and I'm getting dy/dx= (4x+1)^3sin2x.[6cos2x.log(4x+1) + 12sin2x\4x+1]
(edited 6 years ago)
part a= product rule
part b= quotient rule
Original post by Hirsty97
image-dab21d36-7bfc-410a-a9ac-10b975fd079c2003112198-compressed.jpg.jpeg

image-c7ceb54f-e7ca-4039-8efc-e3d82511dee92034104810-compressed.jpg.jpeg


Ohhh your wrong on the answer than, its the product rule... (fg)' = f'g + fg' where f' (f'(x)) is derivative of f (f(x)) same for g and g'; as there is two functions in that equation, but the m and n are the constants which are meant to occur. You know how to do product rule?
(edited 6 years ago)
Reply 6
Avatar for Hirsty97
Hirsty97
OP
21
yeah I do but I thought it was the chain rule

It's been a while since I've looked at C3 erm how do I know whether to use chain, quotient, product rule etc
(edited 6 years ago)
Original post by Hirsty97
yeah I do but I thought it was the chain rule

It's been a while since I've looked at C3 erm how do I know whether to use chain, quotient, product rule etc


Product rule states 2 not 1 outcomes on what it equals to,(fg)′=f′g+fg′ (fg)' = f'g + fg' , don't you revise daily since the beginning?

Quotient rule fg′=f′g−fg′g2 \frac{f}{g}' = \frac{f'g - fg'}{g^2} This should hint out the difference from chain rule as the quotient is used when you need to differentiate a fraction of two different variable functions. Whereas chain rule is used of two different variable function which is NOT a fraction.

You use chain rule when you have a bracket ex. y=(4x+1)3 y = (4x+1)^3 find dydx \frac{dy}{dx} where you sub in u=4x+1,y=u3 u = 4x+1, y = u^3 then differentiate "u= " and "y= " which then dudx×dydu=dydx \frac{du}{dx} \times \frac{dy}{du} = \frac{dy}{dx} Hence the result of the chain rule.
(edited 6 years ago)
Reply 8
Avatar for MR1999
MR1999
21
Original post by Hirsty97
I get that to differentiate it's 12(4x+1)^2 2cos2x

but why does the answer sheet say m=2 and n=12?


You get one mark for getting it into the form in the question and the second for correctly putting the coefficients

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