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 2 years 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>
 2 years 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>

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piscez.in
 2 years ago
Best ResponseYou've already chosen the best response.0find 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!

mathstina
 2 years ago
Best ResponseYou've already chosen the best response.1ok, i tried to work out. is the ans 1?

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

TuringTest
 2 years ago
Best 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...

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

piscez.in
 2 years ago
Best ResponseYou've already chosen the best response.0@mathstina @TuringTest is right

piscez.in
 2 years ago
Best 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

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.1oh yeah, I do get 1 :)

piscez.in
 2 years ago
Best ResponseYou've already chosen the best response.0@TuringTest @mathstina no its not 1, atleast as per my calculations

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

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

piscez.in
 2 years ago
Best 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

mathstina
 2 years ago
Best ResponseYou've already chosen the best response.1Its ok. u too got the same ans

piscez.in
 2 years ago
Best ResponseYou've already chosen the best response.0i got it as 1 previously, now i have 1 :)
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