In calculus, the chain rule is used to differentiate compositions of functions. It states that for any function f which is dependent on a variable u, and u is a function of a second variable x, then f is a function of x.
In Set Theory:
f(u)=u V u(x)=x V Vf(x)
In Calculus:
df/dx = du/dx(dx/du)
In Set Theory:
f(u)=u V u(x)=x V Vf(x)
In Calculus:
df/dx = du/dx(dx/du)
to differentiate (x+1)^2, one could multiply this out and apply the sum rule (derivative of a sum is the sum of the derivatives); but what if it were (x+1)^55? Suddenly the multipling out doesn't look so nice. To apply the chain rule, we must first define the functions. Let f(x)=(x+1)^55 and u=(x+1). Therefore f(x)=u^55. By the chain rule:
df/dx = df/du(du/dx)
df/dx = d/du(u^55)(du/dx)
df/dx = 55u(du/dx)
We earlier defined the variable "u" as (x+1). Now we substitute this in.
df/dx = 55(x+1)d/dx(x+1)
df/dx = 55x+55(1)
df/dx = 55x+55
df/dx = df/du(du/dx)
df/dx = d/du(u^55)(du/dx)
df/dx = 55u(du/dx)
We earlier defined the variable "u" as (x+1). Now we substitute this in.
df/dx = 55(x+1)d/dx(x+1)
df/dx = 55x+55(1)
df/dx = 55x+55
by Gladwarez July 11, 2006
if something exists you can find it or a fake of it on the internet
there is no exception to this rule
there is no exception to this rule
by mikea.c. December 21, 2008
A set of guidelines enacted, usually self-imposed by a coach or manager, to protect a dominant player from being worn out through a long season. One example is one day's rest per each inning pitched.
The GM Cashman of the Yankees perhaps enacted the Joba Rules to prevent manager Joe Torre from wearing out relief pitchers, especially rookie Joba Chamberlain.
by Goddamn Yankees October 03, 2007
Rule 3
by Xeras July 26, 2011
The rule that states "before we go to sleep tonight after smoking this weed, we have to let the incesnse run out." this rule was put into effect because people were smoking and wasting weed because they fell asleep so fast.
"mike: Yo man im so tired, im going to bed"
Steve: Bro if you dont want to owe me money for wasting my weed on your tired ass, you better follow our incense rule"
Steve: Bro if you dont want to owe me money for wasting my weed on your tired ass, you better follow our incense rule"
by Ganjaman1214 June 03, 2010
by C-Gansta July 09, 2003