Directional Derivative – Calculating Derivative oriented by angles – Exercise 4299

Exercise

Calculate the directional derivative of the function

$u=xyz$

At point (1,1,1) and in the vector direction

$\vec{a}=(\cos\alpha,\cos\beta,\cos\gamma)$

What is the size of the gradient of the function at this point?

Final Answer

$D_{\vec{a}} u(1,1,1)=\cos\alpha+\cos\beta+\cos\gamma$

$|\nabla u(1,1,1)|=\sqrt{3}$

Solution

Coming soon…

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