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anonymous
 one year ago
If the derivative of
f[x_] = (x^2  2 Log[x])
f'[x_] = (2x  2/x)
Then why is the derivative of
f[x_] = (x^2  2 Log[x])/2
f'[x_] = (2x  2/x)/2
What is the principle that allows the /2 which appears to be some kind of constant to remain in the derivative ?
anonymous
 one year ago
If the derivative of f[x_] = (x^2  2 Log[x]) f'[x_] = (2x  2/x) Then why is the derivative of f[x_] = (x^2  2 Log[x])/2 f'[x_] = (2x  2/x)/2 What is the principle that allows the /2 which appears to be some kind of constant to remain in the derivative ?

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dan815
 one year ago
Best ResponseYou've already chosen the best response.5because derative is a linear operator

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2constants can be factored out of the derivative

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0wow this guy must be rich to do a QH question

dan815
 one year ago
Best ResponseYou've already chosen the best response.5f[x_] = 2*(x^2  2 Log[x]) heres another example this is same as f[x_] = (x^2  2 Log[x]) + (x^2  2 Log[x]) there are 2 of them, and if u remember we can differentiate each term separately

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no just desperate, lol .. I've given up caring about money

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I just didnt simplify it enough?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5no its not like that its just that the derivative is a linear operator

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0@plasmataco this is calculus ii material

dan815
 one year ago
Best ResponseYou've already chosen the best response.5you can see taking a derivative is a linear operator if you write out the first principles

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0A moderator is present in this conversation. Do not go off topic and break the rules

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0maybe we can try to take the derivatives together.. one is straight forward first it's just derivative and then second is a simple product rule .

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2/2 is division by 2. multiplication or division of a constant to the function, multiplies or divides its derivative by the same constant.. \(\Large if ~ ~f'(x) = g(x), \\ then , ~~ [a \times f(x)]' =a \times g(x) \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah ok.. that's the piece I was missing hartnn

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0even though its a /2 .. it's a constant multiple.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ah ok.. that makes things click for me.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry dan.. that was a colossal effort, much appreciated.. you lost me a bit there though :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.5thats all there is to it, i was showing you why, you can factor the constant out

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0that's why he's the honorary professor of Mathematics XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got to give this one to hartnn though.. that was the piece I was missing.. I knew the /2 had to carry into the derivative, but I could not work out for the life of me, what rule was making that happen.. once I realized it was just a 0.5 f[x] constant multiple, then it clicked..

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0I gave mine to dan, so... yeah, give to @hartnn

UsukiDoll
 one year ago
Best ResponseYou've already chosen the best response.0mine is also given to dan

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2thanks hugh! Its been years i didn't care about medals and stuff, so feel free to give it to anyone you like :)
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