## mathstina Group Title 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

1. piscez.in Group Title

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!

2. mathstina Group Title

ok, i tried to work out. is the ans -1?

3. TuringTest Group Title

what is you function?$f(x,y,z)=\sqrt{xyz}$or$f(x,y,z)=\sqrt xyz$?

4. mathstina Group Title

the first one

5. TuringTest Group Title

$D_{\vec v}=\nabla f(3,2,6)\cdot\frac{\vec v}{\|\vec v\|}$I don't think the answer is one but I haven't done it yet...

6. Algebraic! Group Title

is there an advanced equation editor available to super users that has cool features like gradient?

7. mathstina Group Title

negative one

8. piscez.in Group Title

@mathstina @TuringTest is right

9. piscez.in Group Title

@mathstina first fing the derivative of the function with respect to x, by substituting the y and x values

10. mathstina Group Title

ok

11. TuringTest Group Title

oh yeah, I do get -1 :)

12. mathstina Group Title

ok thanks a lot!

13. piscez.in Group Title

@TuringTest @mathstina no its not -1, atleast as per my calculations

14. TuringTest Group Title

I will show my work and you can spot a mistake if you see one...

15. piscez.in Group Title

ok

16. TuringTest Group Title

$\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$$\frac{\vec v}{\|\vec v\|}=\frac13\langle-1,-2,2\rangle$$\nabla f(3,2,6)\cdot\frac{\vec v}{\|\vec v\|}=\frac16(-2-6+2)=-1$

17. mathstina Group Title

Great!

18. piscez.in Group Title

@TuringTest @mathstina im sorry, your right, i made a mistake by putting all -ves as +ves and vice versa. Bravo you two

19. TuringTest Group Title

cheers!

20. mathstina Group Title

Its ok. u too got the same ans

21. piscez.in Group Title

i got it as 1 previously, now i have -1 :)