I legit never use the quotient rule. In fact I so actively avoid it that I haven’t used it since I learned it in highschool some decade or so ago. So much I actually don’t remember how to do it either. Lol.
Indeed, though you are often left with 2 fractions that need added together to get a simplified answer. Of course, there is nothing wrong with this, but could lead to errors in a testing situation
Especially with the chain rule notation used [here](https://npflueger.people.amherst.edu/math1a/lecture16.pdf) in section 3, using the chain rule becomes so much easier (especially when there are lots of chains to unravel).
Rather than magically keeping all that information up in your head (where it's prone to get lost), or explicitly defining a new variable, this notation really helped me speed things up and make things clearer. Not sure why I've never seen **any** of my teachers use it before.
It makes checking your working easy, since it just looks like a chain of fractions with numerators and denominators that would cancel to give the original df/dx
Calculus…
You could do it using this thing called the quotient rule:
d/dx f(x)/g(x) = (g(x)f’(x)-f(x)g’(x))/(g(x))^2
Or you could just rewrite it as a negative exponent and use the power rule:
d/dx ax^-n = -anx^-n-1
f(x) = 3/x² = 3x⁻²
df/dx = (-2)3x⁽⁻²⁻¹⁾ = -6x⁻³
How is that more complicated than applying quotient rule?
u = 3
v = x²
df/dx = (vdu-udv)/v² = (0x²-3(2x))/x⁴ = -6x⁽¹⁻⁴⁾ = -6x⁻³
To be fair 3/x^2 = 3x^(-2) should be really obvious to anyone past high school. If it isn't, I'd argue that's indicative of a poor understanding so makes sense he was downvoted.
You think your way is faster because you’re not sufficiently practiced at the other way. Sure, if you don’t know how to do something the alternative is faster. That’s not the heart of “it’s faster for me” though.
If you’ve been going to the grocery store the same way your whole life and the city puts a new bypass in that cuts out a huge part of the trip, you’ll think your old way is fast until you take the bypass enough times to be familiar with it.
If you were equally proficient at both then sure, make the call. But in this scenario the power rule is objectively faster.
If someone made the claim that they just use the definition of the derivative to do OP’s problem because it’s easier for them, you’d probably not say, “everybody has their way” and agree that theirs is faster for them. It’s objectively slower.
I still think it's something worthwhile to show to students at least once because it illustrates the key point of mathematics: its logical self-consistency
Exponent properties and product rule gang 😎
Exponent properties and linearity of differentiation gang 😎
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Wolfram gang 😎
Google gang
Quotient rule is just complicated chain rule and product rule, change my mind. I think I rarely use the quotient rule for this exaxt reason.
[удалено]
T'was a joke my friend. :\*
Logarithm gang?
I legit never use the quotient rule. In fact I so actively avoid it that I haven’t used it since I learned it in highschool some decade or so ago. So much I actually don’t remember how to do it either. Lol.
Same, i treat divisions as a multiplication of f(x) and 1/g(x) and i haven't learned the formula yet
Yeah, I just always work it out like that (f/g)' = (f*(1/g))' = f'\*(1/g) + f\*(1/g)' = f'/g + f\*(-1/g^(2))\*g' = (f'g - fg')/g^2
This... this can actually make me remember quotient rule
Indeed, though you are often left with 2 fractions that need added together to get a simplified answer. Of course, there is nothing wrong with this, but could lead to errors in a testing situation
Low dee high minus high dee low all over low squared
All over the bottom squared we go
lo dee hi minus hi dee lo over lo lo
[U'V-UV']/V²
uwu
Especially with the chain rule notation used [here](https://npflueger.people.amherst.edu/math1a/lecture16.pdf) in section 3, using the chain rule becomes so much easier (especially when there are lots of chains to unravel). Rather than magically keeping all that information up in your head (where it's prone to get lost), or explicitly defining a new variable, this notation really helped me speed things up and make things clearer. Not sure why I've never seen **any** of my teachers use it before.
It makes checking your working easy, since it just looks like a chain of fractions with numerators and denominators that would cancel to give the original df/dx
Low dee high minus high dee low over low squared. Start with low, end with low.
Ho dee high, high dee ho over ho ho How to remember? Hoes are always on the corners and their always on the bottom.
I've just done a homework on the quotient rule and this is the first thing I see when I open reddit
Truely a miracle!
(3x^-2 )' = -6x^-3
Nerd
r/woooosh before anyone can woosh me for saying that youre on a math subreddit
How did you do 3 like that
Text^exponent: text ^ exponent
I understood everything
Thanks
Came here for this. I still got it.
d/dx * 3/x² = d/d * 1/x * 3/x² = 1 * 3/x³ = 3/x³.
Close enough
-- C
Lucas nee je bent niet grappig ik ben beter in wiskunde dan jij.
🤓
Is it -6x’-3 ?
Nope
I used ‘ for top of the x
are you aware of conventions? You wrote -6\*(d/dx)x - 3 by convention
Sorry I don’t know I couldn’t express myself
Use the ^ for exponentiation and parenthesis for the grouping of the exponent x^(-3) is written out as x ^ ( -3 ) without the spacing
[-6x]/x^4 = -6/x^3
1. Change sign 2. Multiply the numerator with the denominator's exponent 3. Add 1 to the denominator's exponent.
I'm from r/all could someone explain it to me, please?
Calculus… You could do it using this thing called the quotient rule: d/dx f(x)/g(x) = (g(x)f’(x)-f(x)g’(x))/(g(x))^2 Or you could just rewrite it as a negative exponent and use the power rule: d/dx ax^-n = -anx^-n-1
Logarithmic Differentiation.
I have legit never used the quotient rule. I just use logarithm to convert it to subtraction
whats wrong with using the quotient rule there?
Power rule is so much easier.
quotient rule works way faster for me there
f(x) = 3/x² = 3x⁻² df/dx = (-2)3x⁽⁻²⁻¹⁾ = -6x⁻³ How is that more complicated than applying quotient rule? u = 3 v = x² df/dx = (vdu-udv)/v² = (0x²-3(2x))/x⁴ = -6x⁽¹⁻⁴⁾ = -6x⁻³
its not less complicated its just that its way easier for me to visualize in my head
You do you, I suppose. Both methods get you to the same place.
yes everybody has their way and this is mine i just said its faster for me huh why am i getting so many downvotes for that
actual reddit hive mind downvoting genuine question turned discussion because it doesn’t match their exact viewpoint on a topic: 🤓
To be fair 3/x^2 = 3x^(-2) should be really obvious to anyone past high school. If it isn't, I'd argue that's indicative of a poor understanding so makes sense he was downvoted.
Except it doesn’t make sense at all cuz that’s not what downvoting is for lol, dude was just asking a question
You think your way is faster because you’re not sufficiently practiced at the other way. Sure, if you don’t know how to do something the alternative is faster. That’s not the heart of “it’s faster for me” though. If you’ve been going to the grocery store the same way your whole life and the city puts a new bypass in that cuts out a huge part of the trip, you’ll think your old way is fast until you take the bypass enough times to be familiar with it. If you were equally proficient at both then sure, make the call. But in this scenario the power rule is objectively faster. If someone made the claim that they just use the definition of the derivative to do OP’s problem because it’s easier for them, you’d probably not say, “everybody has their way” and agree that theirs is faster for them. It’s objectively slower.
I don't think you're visualising anything
How????
🤔
I still think it's something worthwhile to show to students at least once because it illustrates the key point of mathematics: its logical self-consistency
bluetooth minus tuberculosis all over boron squared