(3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by integrating along straight lines (i) (x1, y1) → (x2, Y1) then (x2, y1) → (xX2, Y2); and (ii) (x1,Y1) → (X1, Y2) then (x1, y2) → (x2, Y2).

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A: The given function is

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A: To calculate: ddt6r1(t)-4·r2(t) at t=3, where r1(3)=<1,1,0>,…

Q: The total derivative of the function ƒ(x,y) =2x²y– xy is df = (2x² – x)dx +(4xy – y)dy b. df = (4x –…

A: df  = (df(x,y)/dx)dx + (df(x,y)/dy)dy f(x,y) = 2x^2y - xy df(x,y)/dx = 4xy - y df(x,y)/dy = 2x^2 - x

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A: We have to find the directional derivative.

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A: Explanation of the answer is as follows

Q: Derivatives Show that d(y,v)/dv = (1 – v?/c²)-2 for y, = 1/V1- v² /c².

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