What is the difference between a directional derivative and a gradient?

in the directional derivative you are given another unit vector where you find the derivative...





it is the dot product of such a unit vector and the gradient.








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there are two possible gradients you can obtain from a function of more than one variable...





the first is the one giving the steepest ascent (when you dont include the dependent variable)


the next is the one giving the normal vector of a surface when the dependent variable is in the components...

face creams

plumping lip gloss

powder

cooking oil