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Mei C3 differentiation help

How do i differentiate y=x-2/(x+3)^2 and y=(x+1) sqrt(x-1)

The first i've tried using the chain rule then the quotient rule but cannot get the right answer can anyone help and show the working

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Original post by James2015
How do i differentiate y=x-2/(x+3)^2 and y=(x+1) sqrt(x-1)

The first i've tried using the chain rule then the quotient rule but cannot get the right answer can anyone help and show the working


Ambiguous notation on the first.

Product rule on the second.
Reply 2
Original post by Mr M
Ambiguous notation on the first.

Product rule on the second.


First one is (x-2)/(x+3)^2
Original post by James2015
First one is (x-2)/(x+3)^2


Product rule on both then.

You need to know that ddx(ax+b)n=na(ax+b)n1\frac{d}{dx} (ax+b)^n = na(ax+b)^{n-1}
Original post by James2015
First one is (x-2)/(x+3)^2


Use the quotient rule.

Diferentiate (x-2) normally.
Differentiate (X+3)^2 using the chain rule

Then use the quotient rule formula, and factorise etc if applicable.
Original post by Rickstahhh
Use the quotient rule.

Diferentiate (x-2) normally.
Differentiate (X+3)^2 using the chain rule

Then use the quotient rule formula, and factorise etc if applicable.


Unnecessarily complicated.
Original post by Mr M
Unnecessarily complicated.


You can't use product rule on this, as there is not two functions of x multiplied together.

Imo quotient rule is the easiest option
Original post by Rickstahhh
You can't use product rule on this, as there is not two functions of x multiplied together.


Are you sure?

:eek:
Original post by Rickstahhh
You can't use product rule on this, as there is not two functions of x multiplied together.

Imo quotient rule is the easiest option

Yes there are: 11 and x2(x+3)2\frac{x-2}{(x+3)^2}.
Reply 9
Original post by Mr M
Unnecessarily complicated.


I'm still confused with the first equation.

u=(x-2)
u'=1

v=(x+3)^2
v' = 2(x+3)

Sub these into (v*u' - u*v')/(v^2)

Is that right?
Original post by James2015
I'm still confused with the first equation.

u=(x-2)
u'=1

v=(x+3)^2
v' = 2(x+3)

Sub these into (v*u' - u*v')/(v^2)

Is that right?


You can do that but it is long winded. Your work so far is correct.
Original post by Mr M
Are you sure?

:eek:


Yeah, for the question (x-2)/(x+3)^2
As it is a rational function in the form g(x)/h(x), where g(x) and h(x) are functions.

Because , which differentiates to
Original post by Rickstahhh
Yeah, for the question (x-2)/(x+3)^2
As it is a rational function in the form g(x)/h(x), where g(x) and h(x) are functions.

Because , which differentiates to


No way that could possibly be written as a product then (ignoring Smaug's amusing contribution)?
Original post by Rickstahhh
You can't use product rule on this, as there is not two functions of x multiplied together.

Imo quotient rule is the easiest option


You can. Think about negative exponents.

Original post by Smaug123
Yes there are: 11 and x2(x+3)2\frac{x-2}{(x+3)^2}.


Technically correct. Also totally useless.
Original post by james22
Technically correct. Also totally useless.

<doffs cap>
use chain and product together doy
Original post by Mr M
No way that could possibly be written as a product then (ignoring Smaug's amusing contribution)?


Or you could do (x-2)(x+3)^-2
Then use product rule?
Original post by Rickstahhh
Or you could do (x-2)(x+3)^-2
Then use product rule?


That's what I would do. It is usually best to avoid the quotient rule if the denominator is simple.
Reply 18
First equation [(x+3)^2 - (x-2)*[2(x+3)]]/(x+3)^4

has to factor down to (7-x)/(x+3)^3
Original post by Mr M
That's what I would do. It is usually best to avoid the quotient rule if the denominator is simple.


Yeah I totally understand what you mean. I just worked it out using both the quotient and product rule, and tbh the product rule is much much faster

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