anonymous
  • anonymous
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 ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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dan815
  • dan815
because derative is a linear operator
hartnn
  • hartnn
constants can be factored out of the derivative
UsukiDoll
  • UsukiDoll
wow this guy must be rich to do a QH question

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dan815
  • dan815
​f[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
  • anonymous
no just desperate, lol .. I've given up caring about money
anonymous
  • anonymous
so I just didnt simplify it enough?
dan815
  • dan815
no its not like that its just that the derivative is a linear operator
UsukiDoll
  • UsukiDoll
@plasmataco this is calculus ii material
dan815
  • dan815
you can see taking a derivative is a linear operator if you write out the first principles
UsukiDoll
  • UsukiDoll
A moderator is present in this conversation. Do not go off topic and break the rules
dan815
  • dan815
|dw:1434803107603:dw|
UsukiDoll
  • UsukiDoll
maybe 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 .
dan815
  • dan815
|dw:1434803242178:dw|
hartnn
  • hartnn
/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
  • anonymous
ah ok.. that's the piece I was missing hartnn
anonymous
  • anonymous
even though its a /2 .. it's a constant multiple.
hartnn
  • hartnn
exactly!
anonymous
  • anonymous
ah ok.. that makes things click for me.
anonymous
  • anonymous
sorry dan.. that was a colossal effort, much appreciated.. you lost me a bit there though :)
dan815
  • dan815
thats all there is to it, i was showing you why, you can factor the constant out
UsukiDoll
  • UsukiDoll
that's why he's the honorary professor of Mathematics XD
dan815
  • dan815
lol :>
anonymous
  • anonymous
I 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
  • Plasmataco
I gave mine to dan, so... yeah, give to @hartnn
UsukiDoll
  • UsukiDoll
mine is also given to dan
hartnn
  • hartnn
thanks 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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