Mathematics Question Thread

[katnisschung]

yeah..... cos wouldn't that mean
(16,25) and (25,16) would have to be repeated?
as its different to rolling a (25,16)(16,25)
so there would be 9 possibilities??

[RuiAce]

yeah..... cos wouldn't that mean
(16,25) and (25,16) would have to be repeated?
as its different to rolling a (25,16)(16,25)
so there would be 9 possibilities??

Check my correction. I realised I messed up.

[Arisa_90]

what are the rules for differentiating trig and exponential?
I keep getting the questions wrong especially when tan is invovled

[RuiAce]

what are the rules for differentiating trig and exponential?
I keep getting the questions wrong especially when tan is invovled

You have already received an answer regarding a VERY similar question recently.

If you still have problems, please post up example questions and we will point out any mistakes + offer guidance.

[bananna]

(Image removed from quote.)
Here is a simple GeoGebra simulation of the graph, including many important details you have discovered. Note clearly the intercept, turning point and inflexion point provided, as well as the fact that the remainder of the question builds up to the asymptote y=0 for really large negative values of x.

thank you!

[Arisa_90]

Oh sorry. I thought I didn't post this question properly so I accidently reposted it.

You have already received an answer regarding a VERY similar question recently.

If you still have problems, please post up example questions and we will point out any mistakes + offer guidance.

[RuiAce]

Oh sorry. I thought I didn't post this question properly so I accidently reposted it.

It happens. Better check back though.

[Arisa_90]

to differentiate tan doesn't it have to be tanx? = sec^2x x 1?

So for your examples, you find the derivative of the outside and multiply by the derivative of the inside. If we represent these functions as g(f(x)), the derivative is g'(f(x)) * f'(x)
1. The derivative of tan is sec², and the derivative of x² is 2x. So the derivative of tan(x²) is sec²(x²) * 2x. If you want to graph this gradient function, you can see it's always negative when x is less than zero (sec² is always positive) and positive when x>0, but the values fluctuate depending on the x value as cos²(x) is between 0-1
2. Same thing - derivative of tan³ is 3tan²*sec², and the derivative of 2x is 2. So the derivative is
3tan²(2x)*sec²(2x)*2

Try some of the other questions and let me know if there's anything more you want to know / want clarification on

[jamonwindeyer]

to differentiate tan doesn't it have to be tanx? = sec^2x x 1?

That's what you do when you apply the chain rule to the basic tangent function, yes!



Is that what you mean?

[michaelalt]

Hi can someone remind me of how to do q. 13 + 14 of these locus and parabola questions? I forget what everthing is.

[RuiAce]

Hi can someone remind me of how to do q. 13 + 14 of these locus and parabola questions? I forget what everthing is.

Very quickly with Q13 (I'm in a class)

[jakesilove]

Hi can someone remind me of how to do q. 13 + 14 of these locus and parabola questions? I forget what everthing is.

Let's look at 14. We want a point that is always 3 units from the line



When it asks for distance, it always means perpendicular distance. So, we pick any point on the line, and move 3 units away at a perpendicular angle. We can go in either directions, so there will be two points, three units away, for each x value of the initial function. As we move along the function, the dots will move as well. Can you tell what the locus will be?

Clearly, it will be two straight lines, parallel to the initial line, but displaced three units in the perpendicular direction. We use the perpendicular distance formula to find two points, and then use these two point to find the equation of the straight line.





We need this distance to be three, so




Here, we can be smart





This is also obvious from the definition of absolute values. So,




are our two solutions! You'd expect the gradient to be the same (which they are), but the intercepts the be different (again, they are).

Note: There is almost certainly an easier way. If you draw a triangle, you can just figure out how far to the left/right the new lines should shift. Oh well

[cxmplete]

Hi! I'd love your help with question 4)b), I'm confused with what do with the given formula

[Arisa_90]

What would be the best way to differentiate these trig functions?

[Shadowxo]

What would be the best way to differentiate these trig functions?

They want you to use the quotient rule

Hint: derivative of sin(t) is cos(t) and the derivative of cos²(t) is -2cos(t)sin(t) (make sure you know how to do these)