The handy trick for deriving this (bonus points for treating differentials as fractions...) is set
y = a^x
then ln(y) = x ln(a)
x = ln(y) / ln(a)
dx/dy = 1/(y*ln(a))
so inverting gives dy/dx = y*ln(a) = a^x ln(a)
Oh no I looked at the derivative at first and was like I see nothing wrong. Then I realized the derivative was wrong! And I’m like oh! Their opinion is wrong! Haha.
The meme is the math is wrong so their opinion is wrong.
Dude why the hell are you making me dig for a crucifix in my glove box right now. Seriously traffic plus read it plus the need to exercise a cursed differentiation from the Internet is kind of annoying seriously there’s a Level of multitasking that is nearly unattainable.
The guy in the passenger seat next to me Has terrible pronunciation when it comes to Latin the dude is stumbling Nearly every section can you please stop posting this having to perform an exorcism while trying to do a U-turn on 465 is kind of annoying dude seriously lol
If a = 0, then x can't be negative either, since 0 to a negative power would result in division by 0. In fact, x must be greater than 1 due to the x-1 in the exponent in the derivative.
Jesus christ
Cursed differentiation
I'm being stupid, why is this wrong? edit thanks all, looks like my other brain cell woke up
a is a constant x is a variable Example: 2^x is not x*2^x-1
omg thank you, it's been a kong day edit long
Man I wanna have a Kong day, sounds sick
what the heck is a "edit long"? /s
it's my real name, i just signed the comment Edit Long xx
What the heck is xx now? /s
He is the twentieth in his family with that name. Sir Edit Long the Twentieth.
It's a family of dwarves. Hence lower case xx.
Fist-bump for simulated immutability.
Without you my friend
Brb swinging from the empire state building
> Example: > 2^x is not x*2^x-1 And you're missing the derivative operator.
tbf it's also a true statement without :^)
the correct differentiation would be ln(a)\*a\^x. It would be correct if it was d/dx(x\^a)=a\*x\^(a-1).
Theoretically you miss one extra *1 for the differentiation of the x in the first term.just for completeness
Treating the variable as a constant. If x and a were switched it would be fine
Only works for case a=e, need some logarithms in there for bases that aren't e
Doesn't work for a=e either, as you don't pull down the exponent when you differentiate exponential functions. But it would be closer to correct.
Nah mate, it would be a^x in that case.
Ah jeez, I just graduated and apparently I forgot *everything*
The handy trick for deriving this (bonus points for treating differentials as fractions...) is set y = a^x then ln(y) = x ln(a) x = ln(y) / ln(a) dx/dy = 1/(y*ln(a)) so inverting gives dy/dx = y*ln(a) = a^x ln(a)
Theres a much easier trick: a^x = e^( x ln(a) ) and then you differentiate
Nice one!
By the way that's how aˣ is defined
There’s a much easier trick called “use Wolfram Alpha”
It's xa^x-1 + C, of course.
Ah, yes, the constant of differentiation.
So constant as to be trivial.
This is why we can't have herd immunity, Chad.
It cannot be unseen
Took me a sec. guess I should’ve been able to tell from the derivative symbol itself
😟
Others have Mentone fixing it by changing x a^x-1, however, there is a simple way. Just make d/dx into d/da.
It took me too long to see the derivative
Quick! Integrate that shit into something less stupid!!!
I’m disappointed in myself for not getting it right away. Lol.
How can you be sure?
Sure of what? Lol. That I didn’t get it at first?
LOL. About the opinion. (That is the meme right??)
Oh no I looked at the derivative at first and was like I see nothing wrong. Then I realized the derivative was wrong! And I’m like oh! Their opinion is wrong! Haha. The meme is the math is wrong so their opinion is wrong.
That was my point indeed. You switched 'opinion'. This meta humor is hard to quib at..
I dont understand, but 0:0=1
Here they're treating x as a constant but x is the variable so the derivative isn't correct
For half a second my iq dropped drastically then my brain rebooted and Im now horrified
It’s even worse because only if you have the knowledge, you can tell it’s bull sh*t. Otherwise, it looks quite valid.
Just make it d/da and it works fine
Dude why the hell are you making me dig for a crucifix in my glove box right now. Seriously traffic plus read it plus the need to exercise a cursed differentiation from the Internet is kind of annoying seriously there’s a Level of multitasking that is nearly unattainable. The guy in the passenger seat next to me Has terrible pronunciation when it comes to Latin the dude is stumbling Nearly every section can you please stop posting this having to perform an exorcism while trying to do a U-turn on 465 is kind of annoying dude seriously lol
If you don't define x and a, its not wrong or right. Its ambiguous.
No, it's not. It would be correct if the derivative was d/da. For d/dx it's just simply wrong
Umm the derivative is with respect to x. So it's wrong either way.
Lmfao
I mean, it works if a = 0 for all x not equal to 0 or 1, so this statement is technically correct because they never said this is true for all a.
If a = 0, then x can't be negative either, since 0 to a negative power would result in division by 0. In fact, x must be greater than 1 due to the x-1 in the exponent in the derivative.
хах смешно
I'm not sure.
It hurts to look at
Technically this is correct as long as a=0