Maths Methods 3/4 Help Thread 2011

[Tobias Funke]

For composite functions, what defines the domain and range?

[brightsky]

i think you need to work with it case by case. i don't think there is an explicit 'formula' that defines the dom and ran for composite functions.

[pi]

For composite functions, what defines the domain and range?

Well, for fog (or f(g(x)) ) to exist, Ran g must be a subset (or equal to) Dom f. That's pretty much the only 'defining' part of it, as brightsky posted, its fairly case-by-case.

[keahn]

Heyy! Im stuck on this one question whilst doing differentiation, i really need help

i have to derive----> (x^2+1)(2x-4)^1/2

[xZero]

let u = x^2+1, u'=2x, v=(2x-4)^1/2, v'=1/2*(2x-4)^-1/2*2
derivative = u'v+v'u, =(x^2+1)*(2x-4)^-1/2 + 2x*(2x-4)^1/2. you can leave it as this or make it a whole fraction, doesnt really matter.

[ech_93]

Hey,
I'm having trouble differentiating the following with respect to x:

any help would be great

[b^3]

So we have simplified
so

[ech_93]

I need to find x when

All the x's get me confused, and its a non-calculator question...

[xZero]

x=-1? move the square root to the left hand side

[ech_93]

x=-1? move the square root to the left hand side

Oh, wow. That was so obvious, how didn't I realise that -__-

Thanks!

[ech_93]

Another question... I need to differentiate as part of a question. I'm getting by hand, but CAS is telling me
what am i doing wrong

[brightsky]

you forgot the chain rule. multiply the (6x)' = 6 and you've got the answer (expressed in different form).

[xZero]

Hint: chain rule then rationalise it.

[epinephrine]

Infact you don't even need to use the chain rule just break sqrt(6x) into sqrt(6) x sqrt(x) then the sqrt(6)
is just a constant and all you have to do is just derive the sqrt(x) and you'll get the same answer 

[ech_93]

I came across a question; " explain how you can find the derivatives of sin(x), cos(x) and tan(x)?"
How would you go about answering this question? Would you explain how to find it through actually looking at the graph (by this i mean, how you can look at the turning points and they tell you where your x-intercepts are, etc) or a different way?

Please help, thankyou