For directional derivatives:(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex]\hat{u}=<a,b,c>[/itex] be the direction.

Thus, [itex]\frac{∂\hat{u}}{∂x}=\frac{\sqrt{a^2+b^2+c^2}}{a}[/itex] and so on. So,

[itex]\frac{∂x}{∂\hat{u}}=\frac{a}{\sqrt{a^2+b^2+c^2}}=a[/itex]

Thus,

[itex]\frac{∂F}{∂\hat{u}}=\frac{∂F}{∂x}a+\frac{∂F}{∂y}b+\frac{∂F}{∂z}c=∇F \bullet \hat{u}[/itex].

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# Is this derivation valid?

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