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Directional Derivative – Proof that the directional derivative is equal to a certain value – Exercise 4292

Exercise

Prove that the directional derivative of the function

u=\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}

At any point (x, y, z) and in the direction from the point to the origin is equal to

\frac{-2u}{r}

Where

r=\sqrt{x^2+y^2+z^2}

Proof

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