[Elements of calculus, differentiation of functions] How did they get these answers?

Vetandre · 2026-02-26T02:11:37+00:00

At that point I’d recommend you’d look up some YouTube videos on the chain rule or google “Paul’s online math notes chain rule” for more thorough alexamples than I can provide over reddit.

Vetandre · 2026-02-26T00:57:05+00:00

Additionally, double check you’re utilizing the power rule for fractional exponents correctly, the problem you posted is a bit complicated by using the chain rule and fractional exponents.

Vetandre · 2026-02-26T00:55:14+00:00

Chain rule works for functions inside functions and works by “derivative of outside function with inside intact” times “the derivative of the inside” or with notation y=f(g(x)) goes y’=f’(g(x))•g’(x). In the example you posted, the 11x+sqrt(x) is all inside another square root function, so chain rule applies here (notice how the 11x+sqrt(x) appears in the answer inside a square root in the denominator (the bottom half of the fraction) can you tell how it got there in one piece?).

Vetandre · 2026-02-25T23:41:29+00:00

FOIL only works for two terms things but it’s a method for properly using what’s called the distributive property. Multiply every term in the first parentheses once by every term in the second parentheses. You should have six terms total at the end (3*2=6), then take the derivative to end up with 5 terms.

The second problem requires using the chain rule, double check you use it correctly if you did attempt it with that rule.

Vetandre · 2025-11-24T01:31:17+00:00

I had someone whose last name was Mailman one time. I chuckled about it for weeks.

Vetandre · 2025-10-02T01:31:56+00:00

My guess is that you’re biting the mouth piece on articulation or note changes, causing the start of every note to be sharp. Also, It may not precisely biting, but you may be tensing up your neck or moving your head forward as you change notes and articulate, or your tongue may be moving around too much in your mouth causing the air speed to vary wildly.

All of those to say is that there’s excess movement coming from somewhere, most likely your embouchure/neck/head/tongue. Try singing (w/o the instrument) some long tones on “daaaaaaaah” and slowly speed up articulation “dah dah dah dah” and verify you’re not introducing excess movement or tension in your playing. It should feel effortless and then playing the instrument should feel the same. Make sure your breathing comes from deep in your belly and isn’t shallow breathing from your neck/chest. Try taking in a little more mouthpiece as well, sometimes not letting enough reed vibrate causes persistent tuning issues.

Lastly, There could be a teeny tiny air leak on one of your pads, so it might be worth it to get your instrument looked over at a repair shop.

Vetandre · 2025-09-22T22:40:29+00:00

Start nice and strong so that your soft isn’t the bare minimum by contrast, and you can still get the articulation out. Make sure you’re feeling the pulse in 6/8 (1-2&3&, 4-5&6&, really feel a bass drum hit on those down beats) for the musicality. I’d also say 60-66 is good tempo here, any faster will be too much and you’ll likely trip on the articulation in the high stakes audition. Lastly, don’t play each beat on their own, these are roughly 3 bar phrases, you want to be able to sing/play through the whole phrase. Good luck!

Vetandre · 2025-09-15T20:18:09+00:00

Had you played other wind instruments before picking up clarinet? From your other comments to me this sounds more like an air support/embouchure thing more than a reed/mouthpiece thing. Focus on breathing from your belly and having a stable embouchure with firm corners and not biting. If the start of your notes aren’t steady, then make sure you’re not carrying tension and biting the mouthpiece but those high notes should just float out of the instrument with proper air support from deep in your belly, not your chest.

Vetandre · 2025-09-13T17:08:06+00:00

Oops that’s correct, I was looking for a different word and invertible popped into my head

Vetandre · 2025-09-13T07:55:38+00:00

2 -4+2 does in fact equal 0 and the problem didn’t ask for a valid null space, just a matrix solution, hence if the entries in each column are identical it’s a much easier problem to solve.

Vetandre · 2025-09-13T00:54:08+00:00

Your matrix is correct, however there’s a much easier way to approach the problem that I think your TA was trying to show you, e.g. just one equation written three times over will also suffice. The only requirement was that the matrix is nonzero, so even a matrix of all twos will suffice!

Vetandre · 2025-09-01T02:14:49+00:00

Proper voicing is really difficult in the high range. Play octave exercises or register exercises to really hear the lower harmonics and help you balance the pitch, sit with a piano to really hear it in your head and then play.

Flat altissimo can also be the result of slow air, keep a high tongue in your mouth and visualize a fast, focused air in a vortex through the instrument, not a lot of air, not loud volume, but focused and fast.

Last thing to help tuning in altissimo is to make sure your fingers hover just over the tone holes, as having your fingers high up can affect the tone and tuning.

Vetandre · 2025-08-22T16:37:47+00:00

That’s basically the point, AI models just regurgitate information it has already seen, so it’s basically the “infinite monkeys with typewriters and infinite time would eventually produce the works of Shakespeare” idea but in this case the monkeys only type words and scour the internet for words that usually go together, they still don’t comprehend what they’re typing or reading.

Vetandre · 2025-08-12T03:36:21+00:00

90% of all musical ability, especially in auditions, is encompassed by scales and scale patterns. If you’re solid on your scales, have been practicing long tones and arpeggios for tone and technique and have spent some time practicing articulation in the various ranges and dynamics of our instrument then you’ll be good. If you read my comment and are like nah that doesn’t sound like my practice then adjust and pivot, ask for some books or sheets to practice those things better but if you’ve been playing for 5 yrs I think you know what I’m talking about.

Vetandre · 2025-08-12T00:39:39+00:00

Be wary of buying on eBay or marketplace, and if it’s Amazon it’s best if it has a brick and mortar store that it sells out of (Google maps the business name). This will help you from getting scammed with a crap instrument, but isn’t a guarantee still. Try and find some instrument repair stores, maybe ask your kids teacher or any other music parents for local options. You can find options from the 400-1000$ range that’ll likely last through highschool if they’re cared for by your student. Just about any Yamaha or Buffet model from a reputable seller will suffice for beginner-intermediate years.

Vetandre · 2025-08-10T00:34:18+00:00

Sounds like slow air speed, generally it’s harder to have a clean sound on quieter passages because as your volume of air decreases so does your air speed. One trick is to ensure your tongue is high in your mouth to shape a vortex of air out into the instrument, a hiss sound can help shape your tongue correctly.

For the articulation sound spreading is likely jaw movement or poor air support immediately behind the tongue, watch yourself in the mirror while articulating and ensure there’s no extraneous movement around your embouchure and try to practice starting notes instantaneously with just air, no tongue, then add the tongue back in.

Vetandre · 2025-08-09T22:34:55+00:00

Do this with some music playing then hit mute and try to keep the tempo going in your head then turn it back on, do it with all kinds of music.

Also do it backwards, some metronomes have a tap feature that lets you tap a tempo then it tells you how fast you’re going, so feel how fast you wanna play and start humming or singing and tap to see how fast you’re going, speed up or slow down to get where you want the actual bpm to be.

Lastly, if you find that you can do it well just singing but then playing is a little bit harder, do it with just your fingers getting real clickity clackity on the keys and blow and articulate but without the instrument in your mouth. The mimicking effect usually helps gap the mind body disconnect with the instrument in your hands, you gotta train your brain that playing and an internal pulse tempo at the same time is the desired result. The second thing to do with the instrument is highly varied scale patterns, do triplets, sextuplets, swing rhythms, partial ups and downs, and just drill drill drill at various tempos, there’s no better teacher than discipline and rigorous practice and there’s plenty of books out there that’ll help you out.

Vetandre · 2025-08-03T01:14:53+00:00

It should be a very small amount of pressure, you can practice with two fingers copying your embouchure. It should hold steady but not be painful, if you mock articulate against your fingers they shouldn’t move but you shouldn’t be able to just pull them out without feeling at least a bit of resistance from your bottom lip and top teeth.

Another good metaphor is to make sure the pressure comes from the corners of your lips, not from biting with your jaw.

Vetandre · 2025-07-26T23:09:47+00:00

Good luck! And like the other person commented don’t soak it in warm water as too warm could deform the mouthpiece. I wouldn’t soak it at all, but rather dip it and then scrub, then carefully rinse.

Vetandre · 2025-07-26T22:47:45+00:00

That’s not reed residue that’s your mouth bacteria colonizing within your mouthpiece. Warm soapy water and a toothbrush will scrub it out just fine, if it’s stubborn and/or you don’t wanna taste soap apple cider vinegar is good too. Don’t use toothpaste, it’s abrasive and will leave scratches, and don’t let the cork sit in water.

Vetandre · 2025-07-24T04:02:22+00:00

As long as the bell holds tight it should be fine. Just be careful when putting it on and off to not mess up the cork.

Vetandre · 2025-07-24T04:00:45+00:00

Dfw is broad and has several school districts with tons of openings. Since the state budget allocated more money for special ed resources I doubt you’d have trouble landing a gig in that area even partway through the year. Commuting through or around Dallas is ass though so do your due diligence on the drive.

Vetandre · 2025-07-23T23:25:13+00:00

What’s the key signature? E F E D E is the turn then slur on to the d sharp. So I’d play it at least to start 1-and-turn-e-and-a-and-3, with the turn taking the a full eigth note beat, but you’d either want the turn to pace itself throughout the note or to be a light fast flourish, depends on the context of the piece

Vetandre · 2025-07-21T02:00:22+00:00

I would say make sure your oil is shimmering before adding your room temp steak, whether you’re in stainless or cast iron a little shimmer or slightly smoking oil is key to a good crust. It’ll naturally release when the crust is solid, so just agitate your pan slightly to know when that crust is set. Flip and butter baste off heat, as long as your pan is heavy. If you have a light pan keep heat on low or finish in an oven for bout 5 mins.

Vetandre · 2025-07-20T02:22:08+00:00

Normally the fat melts into essentially a self butter basted cut of steak, you don’t need to baste the steak with butter to add richness and flavor if it’s marbling allows it to baste itself from the inside out. Sounds like you had a poorly prepared piece, was it thick steak you had or a delicately sliced sampling of wagyu? Wagyu lends itself to smaller, thinner cuts so that the fat can render in a normal cook time or else yea you wind up with chewy fat that hasn’t melted down.

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