A) Find the directional derivative of the function at the given point in the direction of...

A) Find the directional derivative of the function at the given point in the direction of vector v. f(x, y) = 5 + 6x√y, (5, 4), v = <8, -6>

Duf(5, 4) =

B) Find the directional derivative, D_uf, of the function at the given point in the direction of vector v.

f(x, y) =ln(x²+y²), (4, 5), v = <-5, 4>

D_uf(4, 5) =

C) Find the maximum rate of change of f at the given point and the direction in which it occurs.

f(x, y) =3 y²/x, (2, 4)

direction of maximum rate of change (in unit vector) = < , >
maximum rate of change =

D) Find the directional derivative of f at the given point in the direction indicated by the angle θ.

f(x, y) = 2x sin(xy), (5, 0), θ = π/4

D_uf =

Expert Solution

milcah answered 2 years ago

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