For the function:
y = x^x^x (the superscript notation on this text editor does not work with double superscripts)
To solve for the derivative y', implicit differentiation is needed. First, the equation must be manipulated so there are no x's raised to x's on the right side of the equation. So, both sides of the equation must be input into a natural logarithm, wherein we can use the properties of logarithms to remove the superscripted powers of the right side:
ln(y) = ln(x^x^x)
ln(y) = xxln(x)
ln(y)/ln(x) = xx
ln(ln(y)/ln(x)) = xln(x)
eln(ln(y)/ln(x)) = exln(x)
ln(y)/ln(x) = exln(x)
ln(y) = ln(x)exln(x)
Now there are no functions raised to functions (x's raised to x's). Deriving this equation yields:
(1/y)(y') = ln(x)exln(x)(x(1/x) + ln(x)) + exln(x)(1/x) = ln(x)exln(x)(1 + ln(x)) + exln(x)(1/x) = exln(x)(ln(x)(1+ln(x)) + (1/x))
Solving for y' yields:
y' = y[exln(x)(ln2(x) + ln(x) + (1/x))]
or
y = xx^x
ln(y) = ln(x)x^x
ln(y) = xxln(x)
ln(y) = exlnxln(x)
y'/y = exlnx[ln(x) + 1)ln(x) + exlnx(1/x)
y' = y[exlnx(ln2(x) + ln(x) + 1/x)]
y' = xx^x[exlnx(ln2(x) + ln(x) + 1/x)]
For the function: y = sin(x)cos(x) To find the derivative y', implicit differentiation must be used. To do this, both sides of the equation must be put into the argument of a natural logarithm: ln(y) = ln(sin(x)cos(x)) by the properties of logarithms, this can also be expressed as: ln(y) = cos(x)ln(sin(x)) deriving both sides of the equation yields: (1/y)(y') = cos(x)(1/sin(x))(cos(x)) + -sin(x)ln(sin(x)) This derivative features two important things. The obvious thing is the product rule use to differentiate the right side of the equation. The left side of the equation brings into play the "implicit" differentiation part of this problem. The derivative of ln(y) is a chain rule. The derivative of just ln(y) is simply 1/y, but you must also multiply by the derivative of y, which is y'. so the total derivative of ln(y) is (1/y)(y'). solving for y' in the above, the following is found: y' = y[(cos2(x)/sin(x)) - sin(x)ln(sin(x))] = y[cot(x)cos(x) - sin(x)ln(sin(x))] y' = y[cot(x)cos(x) - sin(x)ln(sin(x))] = sin(x)cos(x)[cot(x)cos(x) - sin(x)ln(sin(x)) is the most succinct form of this derivative.
3 rows of seven with 3 more rows of seven offset by one to the left or right. You end up with all primes. x x x x x x x =x x x x x x x x x x x x x x =x x x x x x x x x x x x x x =x x x x x x x
Get ready, 5 quinquagintillion in Roman Numerals is:(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((V)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))That is 5 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000 x 1000.It's also the same as 5.0 x 10^153
2 x 1004 x 505 x 408 x 2510 x 202 x 2 x 502 x 5 x 205 x 5 x 82 x 2 x 2 x 252 x 2 x 5 x 102 x 4 x 5 x 52 x 2 x 2 x 5 x 52 x 1004 x 505 x 408 x 2510 x 202 x 2 x 502 x 5 x 205 x 5 x 82 x 2 x 2 x 252 x 2 x 5 x 102 x 4 x 5 x 52 x 2 x 2 x 5 x 5
irregular shape! :D x x x x x x x x x x x x
The abbreviation for the word power is "PWR."
Ray Beez has: Played himself in "PWR: Starting a Riot" in 2007. Played himself in "PWR: Reload" in 2007. Played himself in "PWR: Full Throttle" in 2008. Played himself in "PWR: Escalation" in 2008. Played himself in "PWR: The Ties That Bind" in 2008. Played himself in "Captured" in 2008.
Bruce Santee has: Played himself in "PWR: Starting a Riot" in 2007. Played himself in "PWR: Reload" in 2007. Played himself in "PWR: Full Throttle" in 2008. Played himself in "PWR: The Ties That Bind" in 2008. Played himself in "PWR: Declaration of War" in 2008. Played The Marquee Bruce Santee in "PWR: Divide and Conquer" in 2008. Played himself in "FIP: Fallout" in 2009.
Amy Vitale has: Played herself in "FIP: Florida Rumble" in 2004. Played herself in "FIP: Emergence" in 2004. Played herself in "MXPW: Lords of the Ring Tournament" in 2006. Played Kidnapped Russian Girl in "Burn Notice" in 2007. Played herself in "PWR: Starting a Riot" in 2007. Played herself in "PWR: Reload" in 2007. Played herself in "PWR: Escalation" in 2008. Played herself in "PWR: Divide and Conquer" in 2008. Played herself in "PWR: Full Throttle" in 2008. Played herself in "PWR: Uncontrollable" in 2008. Played herself in "FIP: Fallout" in 2009. Played Mars Model - Julie Agrassen in "Planet X: The Frozen Moon" in 2011.
In energy plants, a PWR or Pressurized water reactor, is used as a coolant. The PWR basically stops a nuclear reaction from happening. Also, it keeps water clean from impurities.
Mister Saint Laurent has: Played himself in "PWR: Starting a Riot" in 2007. Played himself in "PWR: Reload" in 2007. Played himself in "PWR: The Ties That Bind" in 2008. Played himself in "PWR: Divide and Conquer" in 2008. Played himself in "PWR: Declaration of War" in 2008. Played himself in "AWA-BCW: Tag Team Turmoil" in 2009.
PWR
You push the ECT PWR button (located left to the radio) to the "Off" position.
Chuck Aurin has: Played Referee in "King of Carnage: Fatal Fourway" in 2003. Played himself in "MXPW: Lords of the Ring Tournament" in 2006. Played Referee in "FIP: Chasing the Dragon" in 2006. Played himself in "PWR: Full Throttle" in 2008. Played himself in "PWR: Escalation" in 2008. Played himself in "PWR: The Ties That Bind" in 2008. Played himself in "PWR: Divide and Conquer" in 2008. Played himself in "PWR: Uncontrollable" in 2008. Played himself in "PWR: Declaration of War" in 2008. Played Andrew in "In Flagrante" in 2011. Played Dean Josson - Mechanical Tech in "Planet X: The Frozen Moon" in 2011. Played Blk Mrkt Zombie in "Play Dead" in 2011. Played Hulking Striker in "Magic City" in 2012.
Power
where is the ect pwr button located on a 1997 avalon? the light came on and my husband assumed he must have pushed a button by mistake.
Francisco Ciatso has: Played Frankie Ciatso in "WWE Velocity" in 2002. Played Frankie Coverdale (2006) in "Deep South Wrestling" in 2006. Played himself in "PWR: Full Throttle" in 2008. Played himself in "PWR: Escalation" in 2008. Played himself in "PWR: The Ties That Bind" in 2008. Played himself in "PWR: Divide and Conquer" in 2008.