How To Find The Directional Derivative and The Gradient Vector

You are always giving angle theta can you plz say with what the function make that angle.ex: like x axis or y axis like that plz reply if anyone also knows

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where are you getting those cos and sine

when finding the unit vector should we always start with sin first or I can start with any of my choice?

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please give background information about issues. You just give formulas

May someone explain the difference between Directional Derivatives and Gradient Vector

everyone in comments are studying this in Cal 3 meanwhile i am studying it in cal 2

Wait, in #3, weren't we supposed to find the magnitude of the vector to make it a unit vector, as we were calculating directional derivative?

thankyou sir

why couldn't my prof teach like this?

Please what would have happened if you were given in 3D the vector in the first question what would have been "c"

yes

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MR. Organic Chemistry Tutor, thank you for a solid explanation on How to Find the Directional Derivative and the Gradient Vector in Multivariable Calculus. This topic is easy to understand from start to finish.