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Find the directional derivatives of the following functions at the given points P in the direction of the vectors v.
f(x,y,z) =√xyz , P (3,2,6) , v =<1,2,2>
 one year ago
 one year ago
Find the directional derivatives of the following functions at the given points P in the direction of the vectors v. f(x,y,z) =√xyz , P (3,2,6) , v =<1,2,2>
 one year ago
 one year ago

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piscez.inBest ResponseYou've already chosen the best response.0
find the derivatives of the function x, y and z seperately, by keeping the other 2 variables constant in each case. Think of a smart way to keep the other 2 variables constant!
 one year ago

mathstinaBest ResponseYou've already chosen the best response.1
ok, i tried to work out. is the ans 1?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
what is you function?\[f(x,y,z)=\sqrt{xyz}\]or\[f(x,y,z)=\sqrt xyz\]?
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
\[D_{\vec v}=\nabla f(3,2,6)\cdot\frac{\vec v}{\\vec v\}\]I don't think the answer is one but I haven't done it yet...
 one year ago

Algebraic!Best ResponseYou've already chosen the best response.0
is there an advanced equation editor available to super users that has cool features like gradient?
 one year ago

piscez.inBest ResponseYou've already chosen the best response.0
@mathstina @TuringTest is right
 one year ago

piscez.inBest ResponseYou've already chosen the best response.0
@mathstina first fing the derivative of the function with respect to x, by substituting the y and x values
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
oh yeah, I do get 1 :)
 one year ago

piscez.inBest ResponseYou've already chosen the best response.0
@TuringTest @mathstina no its not 1, atleast as per my calculations
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
I will show my work and you can spot a mistake if you see one...
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
\[\nabla f=\frac12\langle\sqrt{\frac{yz}x},\sqrt{\frac{xz}y},\sqrt{\frac{xy}z}\rangle\implies\nabla f(3,2,6)=\frac12\langle2,3,1\rangle\]\[\frac{\vec v}{\\vec v\}=\frac13\langle1,2,2\rangle\]\[\nabla f(3,2,6)\cdot\frac{\vec v}{\\vec v\}=\frac16(26+2)=1\]
 one year ago

piscez.inBest ResponseYou've already chosen the best response.0
@TuringTest @mathstina im sorry, your right, i made a mistake by putting all ves as +ves and vice versa. Bravo you two
 one year ago

mathstinaBest ResponseYou've already chosen the best response.1
Its ok. u too got the same ans
 one year ago

piscez.inBest ResponseYou've already chosen the best response.0
i got it as 1 previously, now i have 1 :)
 one year ago
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