2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P in the direction from P to Q. (b) Determine a unit vector in the direction in which T increases most rapidly at P. (c) Find the unit vector in the direction in which T decreases most rapidly at P, and determine the rate of change of T in this direction.

Q: find the directional derivative of f at p in the direction of B.  if f(x,y,z)=x+ycos(z) where p…

A:

Q: Find the directional derivative off at the given point in the direction indicated by the angle 0.…

A:

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: The maximum value of a function f occurs in the direction of the gradient of the function f and this…

Q: Find the directional derivative of f(x, y) = cos(x) + y² at (T,2) in the direction of (3, –4).

A:

Q: Find the directional derivative of the function f(r, y) = xy +x?y? - 2y at the point Po = (2, 1) in…

A: Find the directional derivative of the function at  point.

Q: What is the derivative of a function ƒ(x, y) at a point P0 in the direction of a unit vector u? What…

A: For a function z=f(x,y): the partial derivative with respect to x gives the rate of change of f in…

Q: Find the gradient of y = e" at the point (1, e).

A:

Q: nd the directional derivative of the function f(x,y)=2x²y²+3xy at the point P=(2,-3) in the…

A:

Q: Let r(t) be a vector-valued function such that the magnitude of r(t) does not change over time. Use…

A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: Find the directional derivative of in the direction of the vector (1,3) at the point (-1,2)

A: