Differentiation

y=x/(x+3)^-1/2

so I have differentiated using quotient rule and got:

X/2(x+3)^-1/2 - (x+3)^1/2
---------------------------------
(x+3)

I then multiplied denominator and numerator by 2, to get rid of the fraction.

x(x+3)^-1/2 - 2(x+3)^1/2
--------------------------------------
2(x+3)

This is completely different from the answer at the back):

Reply 1

NNB_Herath

15

Please post a picture of the question or post it in a easy way to read...
:wink:

Reply 2

BULL14

OP

16

Original post by NNB_Herath

Please post a picture of the question or post it in a easy way to read...
:wink:

Simply how would so you differentiate this equation using quotient rule:

y=x/(x+3)^-1/2

Reply 3

NNB_Herath

15

i am confused how this equation looks like ....
is (x+3) a denominator ??
or (x+3)^-1/2 ... a denominator...
Post it clearly please

Is it this ??

Original post by BULL14

Simply how would so you differentiate this equation using quotient rule:

y=x/(x+3)^-1/2

You mean,

\displaystyle \frac x {\sqrt{x+3}}

?

Using the quotient rule, you have

Unparseable latex formula:

\begin{equation*}\displaystyle \frac{\frac{\mathrm d}{\mathrm dx}(x)\sqrt{x+3} - \frac{\mathrm d}{\mathrm dx}(\sqrt{x+3})x}{x+3}\end{equation*}

Looking at your working, it looked like you did it the wrong way around, ie.

g'f -f'g

instead

f'g - fg'

. As a recap, the quotient rule is,

Unparseable latex formula:

\begin{equation*}\displaystyle \left(\frac f g\right)' = \frac{f'g - fg'} {g^2} \end{equation*}

(edited 6 years ago)

Reply 6

tiny hobbit

15

Original post by BULL14

y=x/(x+3)^-1/2

so I have differentiated using quotient rule and got:

X/2(x+3)^-1/2 - (x+3)^1/2
---------------------------------
(x+3)

I then multiplied denominator and numerator by 2, to get rid of the fraction.

x(x+3)^-1/2 - 2(x+3)^1/2
--------------------------------------
2(x+3)

This is completely different from the answer at the back):

As has been said above, you have some errors. Once you have sorted them out, take out a factor of (x+3)^-1/2 from the top (I chose this as the lower power of (x+3)). You will then be able to simplify the bracket that is left.

(edited 6 years ago)

Reply 7

NNB_Herath

15

Post your question clearly ....
This is confusing

Reply 8

arizonaidiot

18

Original post by NNB_Herath

Post your question clearly ....
This is confusing

1.

I'm also taking IAL and wondering if you could help me out.I'm taking the same subjects as you and have just started AS level.Can you tell me what book you used for biology,chemistry and physics.How many hours did you study from october vs nearer to the exams.Whattechnique to you recommend I use if I want to achieve 4as in my AS year(I'm doing maths too).Also,should I use the green student book by ann fulick for biology?Which book is better for physics: Hodder or the red student book by miles hudson? 0

Differentiation

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