Derivatives in Multivariable Calculus

The derivative of f(x,y) in the direction v=(v1,v2), at point p, is:
(fx(p),fy(p))(v1,v2)=v1fx(p)+v2fy(p)

But wait: fx(p) and fy(p) measure how f changes in directions of x and y. Then the formula above claims that knowing only this piece of information, we can know how f changes in any other direction as well?! How could this be true? I will answer this, and end with a eulogy of derivatives in general!

Tuesday, February 5, 2019 - 12:00 to 13:00

Thackeray 703

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Behnam Esmayli