I need help rearranging/manipulating this expression...

ddhurst

Question:

Marking Scheme: (I don't understand what the hell is going on there)

My answer so far:

How do I go from what I've got to the answer I've got to express it in?

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Reply 1

TeeEm

Original post by ddhurst

question:

marking scheme: (i don't understand what the hell is going on there)

my answer so far:

how do i go from what i've got to the answer i've got to express it in?

firstly change all square roots to the power of 1/2

Reply 2

ddhurst

Original post by TeeEm

firstly change all square roots to the power of 1/2

To the *positive* power of a half? Or to either -1/2 or 1/2?

I just noticed you can cancel out the (1/sqrt(1-x)) and the (sqrt(1-x)).

That leaves you with:

((1/2)sqrt(1-x)) (sin^-1(sqrt(x))

That fits with the third line of the marking scheme but I don't see where the (-1) that you have to multiply comes from?

Reply 3

TeeEm

Original post by ddhurst

the marking scheme might not be suitable for a student as it is designed for teacher use.

after the obvious cancellation that you mention
multiply top and bottom of the fraction by √ (1-x)

Reply 4

ddhurst

Original post by TeeEm

the marking scheme might not be suitable for a student as it is designed for teacher use.

after the obvious cancellation that you mention
multiply top and bottom of the fraction by √ (1-x)

I can see why you'd do that; it's called rationalising the denominator, isn't it?

It's just that, with fractions on the denominator and fractions in the numerator, it's getting too messy. And I don't even know what I'm left to work with after the first cancellation.

Can you show me how multiplying by (√(1-x)/(√(1-x)) would play out, please?

I'm not comfortable enough with the algebra yet to go from step to step.

Reply 5

lazy_fish

Original post by ddhurst

...

Check your

\dfrac {d}{dx} \sin^{-1} \sqrt x

(edited 9 years ago)

Reply 6

TeeEm

Original post by lazy_fish

Check your

\dfrac {d}{dx} \sin^{-1} \sqrt x

I do not need to check anything

I have a menacing PDE in front of me and not

\dfrac {d}{dx} \sin^{-1} \sqrt x

Reply 7

lazy_fish

Original post by TeeEm

...

Oops. Apologies. Wrong quote.

Reply 8

TeeEm

Original post by lazy_fish

Check your

\dfrac {d}{dx} \sin^{-1} \sqrt x

lazy_fish suggests your differentiation is wrong

Reply 9

TeeEm

Original post by lazy_fish

Oops. Apologies. Wrong quote.

No worries

could you please take over and help this chap please (unable to multi-task and zero latex skills)

Reply 10

lazy_fish

Original post by TeeEm

...

Sure. Not much left to do except for him to differentiate correctly, I think.
Good luck with your PDE. ^_^

Reply 11

TeeEm

Original post by lazy_fish

Sure. Not much left to do except for him to differentiate correctly, I think.
Good luck with your PDE. ^_^

many thanks

Reply 12

ddhurst

Original post by TeeEm

lazy_fish suggests your differentiation is wrong

Original post by lazy_fish

Sure. Not much left to do except for him to differentiate correctly, I think.

Original post by lazy_fish

Good luck with your PDE. ^_^

I forgot to multiply by the derivative of sqrt(x)?

Should it be:

(1)/(2)(√(1-x))(√x)

So now I'm left with the same expression after substituting in f(x), f'(x), g(x) and g'(x), only that f'(x) is now correct.

So where do I go from there?

(edited 9 years ago)

Bump.

Original post by ddhurst

...

Yes. Correct now. How have you tried simplifying?

Reply 15

ddhurst

Original post by lazy_fish

Yes. Correct now. How have you tried simplifying?

Here's what I've got once I substituted the correct derivative of f(x) in.

Where do I go from here? Please help; I *need* to know this by tomorrow and I can't be up for much longer.

c2?

Original post by coolgamer

c2?

No, it's Scottish Advanced Higher.

Reply 18

lazy_fish

Original post by ddhurst

...

Simplify the expression like you would any other one. Multiply out brackets if it may help. Cancel like terms where possible. Multiply numerator and denominator by something.

Reply 19

ddhurst

Original post by lazy_fish

Simplify the fraction like you would any other one. Cancel like terms where possible. Multiply numerator and denominator by something.

That's why I was asking for help in the first place. I don't know what terms cancel or what on earth to do to get the expressions equal...

Can you please show me and tell me what's happening at each step?