1. ## directional derivatives

$\displaystyle f(x,y,z)=e^{x^2+y^2+z^2}; (1,10,100)$

$\displaystyle \vec{v} = \left[\begin{array}{cc}1/\sqrt{3}\\-1/\sqrt{3}\\-1/\sqrt{3}\end{array}\right]$

$\displaystyle \hat{v} = \left[\begin{array}{cc}1/3\sqrt{3}\\-1/3\sqrt{3}\\-1/3\sqrt{3}\end{array}\right]$

$\displaystyle \nabla f(1,10,100) = 2e^{10101}\hat{i} + 20e^{10101}\hat{j} + 200e^{10101}\hat{k}$

$\displaystyle \nabla f \cdot \hat{v} = \frac{-218e^{10101}}{3\sqrt{3}}$

correct?

2. ## Re: directional derivatives

Did you mean for $\displaystyle \hat{v}$ to be the unit vector in the direction of $\displaystyle \vec{v}$? If so, you are incorrect. $\displaystyle \vec{v}$ is already a unit vector.

3. ## Re: directional derivatives

Originally Posted by HallsofIvy
Did you mean for $\displaystyle \hat{v}$ to be the unit vector in the direction of $\displaystyle \vec{v}$? If so, you are incorrect. $\displaystyle \vec{v}$ is already a unit vector.
thats what I thought but the question says to find the directional derivative in the direction of a unit vector parallel to the given v