Another annoyingly easy question.. (1 Viewer)

[absolution*]

Prelim question..
Ok well.
I have a test first day back next week and im having problems with calculus. Not so much with the rules. (Ie. Product, quotient etc.) but with simplifying once i get the answers.

For eg. My answer was... (4x+9)^4 + 16(4x+9)^3

Back of the book says ---> 32(4x+9)^3 ??
How does this work?

All of them are simplified in the answers so i have no idea.

Yes.. i AM in special ed. Help plz.

 

[loser]

Either your answer or the answer in the back of the book is wrong.

Your answer simplifies to: (4x+9)^3(4x+25) by factorising.

 

[Fosweb]

Post the question.

But usually, even if your answer is one step less simplified, you should get the marks. Unless it actually says: show it equals this...

To get to the answers in the back however, try taking out the highest common factors, such as in your answer, take the (4x+9)^3 and then simplify the rest from there.
However, like loser said, theres a mistake somewhere in there.

 

[jm1234567890]

Originally posted by Fosweb
Post the question.

But usually, even if your answer is one step less simplified, you should get the marks. Unless it actually says: show it equals this...

To get to the answers in the back however, try taking out the highest common factors, such as in your answer, take the (4x+9)^3 and then simplify the rest from there.
However, like loser said, theres a mistake somewhere in there.

my 4unit teacher took makes off for a correct answer that wasn't simplified as much as he wanted

 

[redslert]

Originally posted by absolution*
(4x+9)^4 + 16(4x+9)^3

wasn't fully simpify

(4x+9)^4 + 16(4x+9)^3
take out (4x+9)^3
(4x+9)^3 [4x+9+16]
simpify
(4x + 25).(4x+9)^3

your answer is wrong....or the back of the book is wrong....or it's too early in the morning

 

[Fosweb]

Originally posted by jm1234567890
my 4unit teacher took makes off for a correct answer that wasn't simplified as much as he wanted

Thats slack and usually beside the point of the questions. (Like - you spend however long getting to the answer, so you shouldnt lose marks in 4U for not simplifying...)

 

[redslert]

i dont think your teacher actually took marks away

i think it is more of, you didnt get any for the final answer

 

[LadyMoon]

Do you mean
y=(4x+9)^4?
and therefore differntial is =16(4x+9)^3???

 

[absolution*]

Ok..
i was wrong as usual.
My bad.
But for example with a question such as:

(2x-9)^3 / 5x+1

How would you simplify that fully?
I dont understand the whole common factor thing.
And in our half yearlies we lost marks for not simplifying fully hence me asking for help.

 

[redslert]

Originally posted by absolution*
(2x-9)^3 / 5x+1

this is fully simplify already

you cannot make it any more simple, unless you want to expand the brackets which isn't simplifing

did you just make that up? i think you did......

 

[absolution*]

No i meant that is the full question to differentiate. DEr~!
I can differentiate it just not simplify it after using the quotient rule.

 

[redslert]

in that case

f(x) = (2x-9)^3 / (5x+1)
.'.
f'(x) = [6(2x-9)^2 * (5x+1) - 5(2x-9)^3] / [(5x+1)^2]

= {(2x-9)^2 * [6(5x+1) - 5(2x-9)]} / [(5x+1)^2]

= {(2x-9)^2 * [30x + 6 - 10x + 45]} / [(5x+1)^2]

= {(2x-9)^2 * [20x + 51]} / [(5x+1)^2]

i would leave it there, if you go any further it's gonna get ugly!

 

[absolution*]

Ok i think i get it.
Would it be easier just letting the brackets equal pronumerals?
Then simplifying?
Then subbing back in???

 

[LadyMoon]

Originally posted by absolution*
Ok i think i get it.
Would it be easier just letting the brackets equal pronumerals?
Then simplifying?
Then subbing back in???

yeah if you find it easier...but with practise soon you'll find that you wouldnt need the pronumerals. But yes...when i was in prelims it did seem like a good option.

but when you get to the hsc, you gotta get rid of that!

 

[redslert]

just imagine them as pronumerals....
cause if you gonna change things around....it increases the possiblity of making a silly mistake
plus it's gonna take you longer to do a given question

 

[kimmeh]

some books posts wrong answers..what book is this?

 

[shkspeare]

on the topic of differentiation
some1 differentioate

x sqrt(x+1)
or x(x+1)^(1/2)

im stuck >.<

 

[evilc]

First rewrite xSQRT(x+1) as: x(x+1)^(1/2)
then use product rule:
d/dx (uv) = vu' + uv'

so,

d/dx x(x+1)^(1/2) = 1*(x+1)^(1/2) + x*(1/2(x+1)^(-1/2))

= (x+1)^(1/2) + x / 2(x+1)^(1/2)

= SQRT(x+1) + x / 2SQRT(x+1)

 

[redslert]

Originally posted by evilc
d/dx x(x+1)^(1/2) = 1*(x+1)^(1/2) + x*(1/2(x+1)^(-1/2))

= (x+1)^(1/2) + x / 2(x+1)^(1/2)

i would take it further:

= (x+1)^(1/2) + x / 2(x+1)^(1/2)

multiply both sides by (x+1)^(1/2)

= (x + 1 + x) / (x+1)^(1/2)

= (2x + 1) / (x+1)^(1/2)

= (2x + 1) * (x+1)^(-1/2)

hmmmm sorry if i complicated it
but i was taught always to leave the final answer in the format of the given question....unless otherwise stated...

so the question was in one line, the solution shall be the same

 

[:: ck ::]

redslert your final answer is wrong
try substituting x = 3

you should end up with 2 and 3/4