What is the gradient vector of the function
f(x,y,z)= 9 SQRT(x^2+y^2+z^2)
Ive tried to solve it several different ways and i still can figure it out, i think im not converting the SQRT to exponents correctly.|||grad F = 鈭侳/鈭倄I + 鈭侳/鈭倅J + 鈭侳/鈭倆K
I,J,K are usual unit vecdtors.
鈭侳/鈭倄 = 鈭?鈭倄[9鈭?x虏 + y虏 + z虏)]
= 9[1/2 (x虏 + y虏 + z虏)^-1/2 X(2x)]
鈭侳/鈭倄 = 9x / 鈭?x虏 + y虏 + z虏)
By symmetry
鈭侳/鈭倅 = 9y / 鈭?x虏 + y虏 + z虏)
鈭侳/鈭倆 = 9z / 鈭?x虏 + y虏 + z虏)
gradF = [9x /鈭?x虏+ y虏+z虏)]I + [9y /鈭?x虏+y虏+z虏)]J + [9z /鈭?x虏+y虏+z虏)]K
= [9 / 鈭?x虏+y虏+z虏)] [xI + yJ + zK]
Remember vector %26lt; r %26gt; = xI + yJ + zK
also r虏 = x虏+y虏+z虏
so r = 鈭?x虏+y虏+z虏)
Hence gradF = 9(%26lt; r %26gt; / r)
Note: there is no easy way to represent vectors here so I have
used %26lt; r %26gt; to represent actual vector and r to represent magnitude of vector.
Subscribe to:
Post Comments (Atom)
Harrah's Cherokee Casino and Hotel - Mapyro
ReplyDeleteHarrah's 동해 출장샵 Cherokee Casino 아산 출장마사지 and Hotel is located 영천 출장안마 in Cherokee, North Carolina 광명 출장샵 and is open 천안 출장샵 daily 24 hours. The casino, located on 217 acres along the