Question

Compute the directional derivative of *f* at the given
point in the direction of the indicated vector.

*f*(*x*, *y*) =
*e*^{4x2 − y}, (1, 4),
**u** in the direction of −4**i** −
**j**

*D*_{u}*f*(1, 4) =

Answer #1

Find the directional derivative of f at the given point
in the direction indicated by the angle θ.
f(x, y) = y cos(xy), (0,
1), θ = π/4

Find the directional derivative of the function f (x, y) =
tan−1(xy) at the point (1, 3) in the direction of the unit vector
parallel to the vector v = 4i + j.

find the derivative of the function f at the given
point P in the given direction u.
f(x,y,z)=zarctan(y/z)
P(3,-3,1)
u=4i-j+3k

Find the directional derivative of the function at the given
point, in the
vector direction v
1- f(x, y) = ln(x^2 + y^2 ), (2, I), v = ( - 1, 2)
2- g(r, 0) = e^-r sin ø, (0, ∏/ 3), v = 3 i - 2 j

Find the directional derivative of the function at the given
point in the direction of the vector v.
f(x, y, z) = x2y + y2z, (2, 7, 9), v = (2,
−1, 2)
Dvf(2, 7, 9) =

Find the directional derivative of the function at the given
point in the direction of the vector v.
f(x,y,z)= x2y3+2xz+yz3
(-2,1,-1) v= <1,-2,2>
Use the chain rule to find dz/dt. z=sin(x,y) x= scos(t)
y=2t+s3

Compute the directional derivative of the function
f(x,y)=(√1+3x^2+8y^2) at the point (0,−3) in the direction of the
vector →v=2ˆi−3ˆj. Enter an exact answer involving radicals as
necessary.

Let f(x y z)=x4y4+z5,
P=(4, 4, 1).
Calculate the directional derivative in the direction pointing
to the origin. Remember to normalize the direction vector.
(Use symbolic notation and fractions where needed.)
Duf(4, 4, 1)

Let f(x y z)=x4y4+z5,
P=(4, 4, 1).
Calculate the directional derivative in the direction pointing
to the origin. Remember to normalize the direction vector.
(Use symbolic notation and fractions where needed.)
Duf(4, 4, 1)

1. Let f(x, y) = 2x + xy^2 , x, y ∈ R.
(a) Find the directional derivative Duf of f at the point (1, 2)
in the direction of the vector →v = 3→i + 4→j .
(b) Find the maximum directional derivative of f and a unit
vector corresponding to the maximum directional derivative at the
point (1, 2).
(c) Find the minimum directional derivative and a unit vector in
the direction of maximal decrease at the point...

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