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- anonymous

Find the directional derivative of \[f(x,y,z) = yz + x^4\] at (2,3,1) in the direction of vector v=i+j+k.
I have gotten as far as finding the directional derivative (gradient) at (2,3,1) which is:
32i+3j+k
I dont know how to do the second part of this problem. What does it mean to find this direction? What do I have to do to the gradient to find it? My book is very vague, please help!

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- anonymous

- schrodinger

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- anonymous

Tips?

- anonymous

The box for the answer says fu= _____ , where u looks like a unit vector, is that what this is asking for? A unit vector of the gradient?

- anonymous

Never mind, that, I tried, and was told my answer should be a number, not a vector. Guess I misinterpreted that.

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- UnkleRhaukus

\[
\newcommand \ve [1] { \mathbf{#1} }% vector
\nabla_{\ve v}f(\ve x)=\nabla f(\ve x)\cdot{\ve v}\\
\
\\
f=yz+x^4\\
\ve v=(1,1,1)\]

- anonymous

I think I understand what you wrote, but it still isnt clear to me what "in the direction of" means... I can find the gradient just fine, I've just no idea what to do with it.

- UnkleRhaukus

once you have found the gradient, take the dot product with the direction vector

- anonymous

ahhhhh, that makes sense, thank you!

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