VCE Specialist 3/4 Question Thread!

[Brunette15]

Can someone please show me how to differentiate 2/(1+4x^2)...I don't know where I am going wrong

[lzxnl]

Can someone please show me how to differentiate 2/(1+4x^2)...I don't know where I am going wrong

2/(1+4x^2) = 2(1+4x^2)^-1
Using chain rule, the derivative of this is 2*8x*-1*(1+4x^2)^-2 = -16x/(1+4x^2)

[Brunette15]

2/(1+4x^2) = 2(1+4x^2)^-1
Using chain rule, the derivative of this is 2*8x*-1*(1+4x^2)^-2 = -16x/(1+4x^2)

Ah yes thankyou! I was attempting to use quotient rule   

[keltingmeith]

Ah yes thankyou! I was attempting to use quotient rule   

Welp, if you want to use the quotient rule:



The thing with differentiation rules is that they always work (at this level, at least), so don't worry about picking "the wrong one" like you can with integration techniques.

[lzxnl]

Welp, if you want to use the quotient rule:



The thing with differentiation rules is that they always work (at this level, at least), so don't worry about picking "the wrong one" like you can with integration techniques.

At what level would they not work? I can't imagine a function in which you can't differentiate it without chain rule and need to use product rule or something.

[keltingmeith]

At what level would they not work? I can't imagine a function in which you can't differentiate it without chain rule and need to use product rule or something.

Honestly, I'm more just covering my arse because I can't say I've done enough analysis to know that these rules always work for everything.

[Brunette15]

Honestly, I'm more just covering my arse because I can't say I've done enough analysis to know that these rules always work for everything.

Thankyou 

[Brunette15]

Can someone also please help me with this question:

Find all solutions of z^4 -2z^2+4=0, z E C in Cartesian form.

I have attached my working out so far but got a bit stuck :/

[shadows]

random question
do you need to include the tilde (that squiggly line at the bottom for vectors) for momentum or force (p or F) when it only includes constants (no i and j)

Cause I recall my teacher saying that you always need to include it in vectors.

[Sanguinne]

VCAA 2006 Exam 2 Question 2c))

Find the cosine of angle ABC and hence show that angle ADC and ABC are supplementary

from previous part angle ADC = 4/5
i correctly worked out angle ABC =-4/5

however to show their supplementary, is it sufficient to show cos(angle ADC + angle ABC) =-1
 and therefore angle ADC + angle ABC = pi or otherwise 180 degrees??

[yang_dong]

hello,
the ans says A, but then that would be completely ignoring the 21% info?

Thank you

[silverpixeli]

yep, the 21% info is not used in this question. It's an initial value, and would only be used if you went on to solve the differential equation to determine your constants of integration and whatnot! The differential equation is independent of this initial condition and just depends on the input and output rates.

[lucas.vang]

Can someone please explain how I would justify 2c

ty

[RKTR]

Can someone please explain how I would justify 2c

ty

cos(pi-x)= -cos(x)
cos(pi-ABC) =0.8
cos(ADC)=0.8

pi-ABC=ADC
ADC+ABC =pi therefore they are supplementary angles

[lucas.vang]

Thanks