Question

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

Answer #1

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

Find the directional derivative of the function at the given
point in the direction of the vector v. h(r, s, t) = ln(3r + 6s +
9t), (2, 2, 2), v = 14i + 42j + 21k

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
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→

Find the directional derivative of the function
f(x,y,z)=ln(x2+y2−1)+y+6z at the point (1,1,0) in the direction of
the vector v→=i→−2j→+2k→.

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 directional derivative of the function at P in the
direction of v. f(x, y) = x3 − y3, P(8, 5), v = 2 2 (i + j)

Compute the directional derivative of f at the given
point in the direction of the indicated vector.
f(x, y) =
e4x2 − y, (1, 4),
u in the direction of −4i −
j
Duf(1, 4) =

Find the directional derivative of the function
f(x,y)=x^6+y^3/(x+y+6 ) at the point (2,-2) in the direction of the
vector < - 2 ,2>.
b) Also find the maximum rate of change of f at the given
point and the unit vector of the direction in which the maximum
occurs.

find the directional derivative of f (x, y) = x ^ 2 in the
direction of v = i-j for the point (-1,2).

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