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mathcalculus
 2 years ago
can someone explain this simple derivative to me please: sort(6x)
mathcalculus
 2 years ago
can someone explain this simple derivative to me please: sort(6x)

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mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0isn't it 1/2(6x)^(1/2)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0how does it go from there to the answer: sqrt(6)/2 sqrt(x)

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1It's chain rule so you also need to multiply by the derivative of the inside. So it would be what you put, but then multiply by 6.

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{6x} = \frac{ 1 }{ 2 }(6x)^{\frac{ 1 }{ 2 }}(6)\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0im no sure about the chain rule its confusing

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i know its: [f(g(x))]'= f'(g(x))*g'(x)

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Well, I have a unique way of showing it, so maybe it will help maybe not. Were you one of the ones I sent the derivative files to?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait, i think so a while ago.

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Ah xD Yeah, one of them had the chain rule in it. I teach it in a unique way, so maybe it helps maybe it doesn't.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0does it always work?

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah. As long as you recognize what layers you have then yeah. Chain rule is multiplying the derivatives of each layer you have, making sure to not disturb what was originally inside of each layer.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thanks im going to read it right now

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0ugh i gave it a shot. wrong. :(

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Well, you bring the power down and then you made the power become 1/2. You're done with that layer, now you just go to the inner layer. \[\frac{ 1 }{ 2 }()^{\frac{ 1 }{ 2 }}\] Thats it, no more to that part.

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Well, when you do the outer layer. All you do is bring the power down as a multiplication then lower the power by 1. After that you are done with that layer. There's no other 1/2 to multiply by.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0down in the denominator?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0can you show me the steps to the answer? just want to see how you did it so i can ask

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Alright, so we have two layers. The first layer is simply ( )^1/2 and the inner layer 6x. So the chain rule says that we take the derivative of each layer and multiply the results. So following the normal derivative rule of \[\frac{ d }{ dx }k ^{n} = nk ^{n1}\], I'll do that with the first layer. \[\frac{ 1 }{ 2 }()^{\frac{ 1 }{ 2 }}\]I just left the inner part blank for now, but that is the derivative of the first layer. Now I do the second layer, which is just 6x. So the derivativeof 6x is simply 6. So now that I have the derivative of both layers, I now multiply both of these derivatives \[\frac{ 1 }{ 2 }()^{\frac{ 1 }{ 2 }}*(6)\] This of course becomes: \[\frac{ 3 }{ ()^{\frac{ 1 }{ 2 }}}\] Now all that is left to do is plug back in what was originally inside of that layer, giving us: \[\frac{ 3 }{ \sqrt{6x} }\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh the answer is sqrt (6)/2 sqrt(x)

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1It's the same thing actually xD

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1I'll show ya why: \[\frac{ 3 }{ \sqrt{6x} }=\frac{ 3 }{ (\sqrt{6})(\sqrt{x)} }\]Now multiply top and bottom by sqrt(6) \[\frac{ 3(\sqrt{6)} }{ (\sqrt{6})(\sqrt{x})(\sqrt{6}) }\]This then becomes finally: \[\frac{ \sqrt{6} }{ 2\sqrt{x} }\]

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0alrigght thanks ! :)))

Psymon
 2 years ago
Best ResponseYou've already chosen the best response.1Mhm, np ^_^ Hope that made sense xD
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