Can a directional derivative be negative?

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I just calculated the directional derivative of a function and ended up with $- \frac{1}{3}$ which seems counterintuitive. Can this be possible?

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2 Answers

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Yes. Directional derivative is the change along that direction, it could be positive, negative, or zero. The directional derivative being negative means that the function decreases along that direction, or equivalently, increases along the opposite direction.

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Yes, for example partial derivatives are directional derivatives. And partial derivatives can be negative.

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