Find the directions in which the function increases and decreases most rapidly at Po. Then find the derivatives of the function in these directions f(x,y,z) = (x / y) – yz, Ро(4,1, - 3)

Q: Find the directional derivative of the function xy2 + yz2 + zx² along the tangent to the curve x =…

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Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y, z) = xy + yz + zx, P0(1, -1,…

A: Given: To Find: The derivative of the function at P0 in the direction of v. Concept:

Q: compute the derivatives indicated. g(x, y, z) = x*y°z°, 8xxyz

A: The expression gx represents the partial derivative of g with respect to x. Subsequent sub-notations…

Q: Find the directional derivative of f(x,y) = 2x –y´ at the point (1, 3) in the direction toward the…

A: We have given f(x, y) = 2√x – y2 and the point (1, 3).

Q: Find the derivative of the function using the definition of derivative. dy = lim dx Ar-0 Ar Ay 1.…

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Q: Find the directions in which the directional derivative of f (x, y) = ye*y at the point (0,2) has…

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

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Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: Find the derivative of the function at P0 in the direction of u. f(x, y) = 3x 2 + 4y, P 0(8, 7),…

A: Directional derivative: - The rate at which any function changes at any given location in a fixed…

Q: Find the derivative of the function f(z, u) = =*y – 4y° at the point Po(2, 1) in the direction of =…

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Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: (a) Find the derivative of fix. y. 2) = x-xy-z at P1, 1,0) in the direction of v = 2i- 3j + 6k. (b)…

A: The directional derivative of a function f(x,y,z) at the point (x,y,z) in the direction of vector v…

Q: find the derivative using the appropriate rule or combination of rules. y = (z + 1)4(2z − 1)3

A: The given function is y = (z + 1)4(2z − 1)3

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: Find the derivative of the function at P0 in the direction of u. f(x, y, z) = -9x + 3y + 8z, P…

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Q: Evaluate the directional derivative of the function f =x² - y° + 2z? at the point A (1,2,3) in the…

A: The directional derivative of a function f at a point a in the direction of a vector v is…

Q: Find the derivative of the function at Po in the direction of u. f(x, y, z) = In(x 2 + 3y 2 + 9z 2),…

A: Given that      f(x,y,z)=ln(x2+3y2+9z2), P0(3,3,3), u=3i+4j Here we have to find the derivative of…

Q: Use differentiation to find the gradient of the curve y : = ax sin(bx) at x = 3.

A: The solution is given as

Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: Find the derivative of the function at Po in the direction of A. f(x,y,z)=3 ex cos (yz), Po(0,0,0),…

A: Solution: f(x,y,z) =3exCos(yz) P0=(0,0,0)

Q: Find the derivative of the function. 2x y = /3 cos(x) m cos(u") du y' =

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

A: Definition used -          Directional derivative at the point -     The rate of change of f(x, y)…

Q: Find the derivative of the function f(z,k) = z^4— 16k^3+ tanh(z) — 4 csc(k) in terms of z and k ?

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Q: Find the directional derivative of f(x, y) = x 2 + 4y 2 at the point P = (3, 2) in the direction…

A: Given, f(x,y)=x2+4y2 at the point P=(3,2)

Q: Find the directional derivative of the function at point P in the direction of v. 3 u = 4 f(x, y) =…

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Q: Find the directional derivative of the function f(x, y) = x² + y³ at the point (2, 1) in the…

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Q: Find the derivative of the function at Po in the direction of u. f(x, y) = In(-10x - 7y), P o(-4,…

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Q: Find the derivative of the given function at the point (a, a?, a) in the direction of w = ai + 2aj +…

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Q: Find the directional derivative of f (x, y) = e" /Ty at the point (1,16) in the direction of the…

A: From the given problem:   fx,y=exxy ; p1,16   And the direction of the negative y- axis means :…

Q: 24. f(x, y, z) = xy² z³, P(2,1, 1), Q(0, –3, 5)

A: Given function is   f(x,y,z)=xy2z3 P(2,1,1), Q(0,-3,5)

Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

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Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: Find the derivative of the function at Po in the direction of u. x- 5y g(x,y) = Ро(1, - 1), и%3 3і +…

A: To find the derivative of the function  g(x,y)=x-5y5xy+7 at P0(1,-1)in the direction of…

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2xy - 3y2, P0(5, 5), u =…

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Q: Find the derivative of the function at Po airection oT u. f(x, y) = 3x 2 + 4y, P o(8, 7), u = 3 i -…

A: 1. Given f(x, y) = 3x2 + 4y and u = 3i - 4j u^ = 1|u|u = 15(3i - 4j) ∇f·u^ = (i^ddx(3x2+4y) +…

Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: f(x, y) = e2Y sin(x), P(0, 0), Q(2, 1)

A: Use the formula for the directional derivative and simplify.

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = 4xy – 4y“, Po(-2, - 8), A…

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Q: 21: dz 22: Find the derivative of f(y,x) = xe?y + cos(3yx) at a point (1,0,7)in the direction of V =…

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Q: Find the derivative of the function at P,(0,0,0) in the direction of B. f(x, y,z) = 3e* cos yz,…

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Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: Find the directional derivative of the function at P in the direction of v. f(x, y) = 8x-4xy+3y,…

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Q: Find the derivative of the function at Po in the direction of A. f(x, y, z) = xy + yz + zx, Po(1,…

A: Given query is to find direction derivative.

Q: Find the unit direction vector of greatest decrease of f at xo = [0 - 1 1]' and evaluate the…

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Q: Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in…

A: Given thta  f(x,y,z)=x/y+y/z+z/x  To find teh derivative of the function at point p in the direction…

Q: Find all second order derivatives for r(x,y) = ху 5x+ 2y Tox(x.y) = U

A: