Math revision

NuclearVision

Some math revision will be good,
Differentiate the following :

This is a medium difficulty derivative
I won´t post my solution, because if i did the topic will be mind-challenging-less.
More are coming soon.

And could anyone tell me which student level is that ?

geek

most probably grade 11–12. this is more of a calculus monkey exercise than a medium difficulty mind challenge.

Joe

This is the kind of math I did in my last year of high school, and this is only because of the exponential and logartihm. The derivative formulas are taught the year before or the one before that. So are trig functions.

I'll try to give you my solution this afternoon.

NuclearVision

I did it using pencil and paper:
Yesterday i found a pdf book for differentiation, understood basics of calculus, then started messing with those. I could not understand the whole thing because in my school they teach mathematics in french(grade 9)
Book: here
And geek, what do you think is a ¨medium difficulty calculus exercice¨? I think you´re a bit picky man.

Joe

It's not a particularly difficult exercise because it's simply applying straightforward formulas. There's a lot to apply but they are pretty straightforward, very little cleverness involved.

This is why he called it "calculus monkey" exercise.

NuclearVision

rahmu wroteIt's not a particularly difficult exercise because it's simply applying straightforward formulas. There's a lot to apply but they are pretty straightforward, very little cleverness involved.

This is why he called it "calculus monkey" exercise.

Yep, youŕe both right. I think it is rather long than difficult.
Have you got any more difficult one? But please make it a short one regardless its difficulty level :D

geek

you're a 9th grader? courage and cheers!
mind challenge is tightly associated with insight, if there's no insight, there's no challenge.
the exercise you posted is very mechanical; it's not your fault though—mathematics is rarely taught by example in our schools, even colleges.
it would be nice to see how the formula was derived and what does it, and thus its derivative, represent. as you will see later on, the main challenge (in most cases) is in deriving these formulas, not solving them.

mesa177

The difficulty level on this one is easy, not medium, because as geek and rahmu pointed out, it is a straight forward application to formulas. However, it being a grade 12 level problem (exponential, logarithm, inverse trigonometric functions are taught at that level), and you being a 9th grader, I can see why you regard it as medium level. PS: Kudos and respect for the plunge you took :)

Seeing that writing the solution would be extensive and I simply lack the effort to do it today, I can state my solution approach as follows:

Knowing that:

f'(u/v) = [u'v - v'u] / v^2 (where both u and v are functions of x, and the derivation is done corresponding to variable x)
(e^u)' = u' . e^u
ln'(u) = u'/u
(arccos(x))' = -1/sqrt(1-x^2)
(sqrt(u))' = u'/2.sqrt(u)
cot(x) = 1/tan(x)

And of course after defining the domain of the definition (I'm too lazy to find it out right now, but it has to be specified before proceeding with the solution)

The final solution will be:

Don't know if it can be reduced any further than that...

Also, a while ago I posted a couple of math exercises for grade 12 students to solve. You can check them out if you want.

hussein-berjaoui

I can't even handel reading this..

arithma

I find the best calculus problems to be rooted in physics. Get yourself any physics word problem and try to solve it using calculus. Usually those will create insight into the problems and will reinforce the way you deal with calculus itself.

My two cents.

Joe

hmmm good luck coming up with a physics problem modeled by the above equation...

arithma

That's exactly my point. The above equations are absurd beyond recognition. And they're very hard to get a feel off. Physics problems on the other hand will be penetrable to insight "through" the equations. The equations will be valuable in that retrospect.

Here's a little problem I don't know the solution of exactly:
We hit a light ray of a single wavelength at a crystal. The crystal has the special property of an increasing index of refraction as you go deeper into it (linearly). Derive the path of light through the crystal accounting for all unspecified variables.
Derive another equation if the change of the index of refraction is to be later specified using a function
f: distance -> index of refraction.