Let f(x, y) = x 3y - 4 . Use Eq. (4) to estimate the change fl.f = f (2.03, 0.9) - f(2, 1)

Q: Find the directional derivative of z = f (x, y) = x²y³ – 3y² at (-3,4) in the direction of the…

A: Use directional derivative formula which is mentioned in solution.

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y, z) = x2 + 2y2 - 3z2, P0(1,…

A: f(x,y,z) = x2 + 2y2 -3z2  v = i + j + k  P0(1, 1, 1)

Q: Find the derivative of the function f(x,y,z) = x² + 2y² – 3z² Po = (1,1,1) in the direction of at…

A:

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

A: Note: where △f(x,y) = ∂f∂x,∂f∂y

Q: Find the directional derivative of f(x, y) = (xy)^1/2  at P(6, 6) in the direction from P to Q(9, 2)

A: The directional derivative (D.D) of function f at point P in the direction of vector a is given by,

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

A: Given,

Q: O Find the directional derivative of f(x, y) = 3x² – 3y² in the direction from P(-,0) to Q(0, 1).

A: Point is given so first find the direction unit vector then  dot product with divergent of f(x,y)…

Q: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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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).

A:

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: The equation of line normal to f(x) = (x +4)^(1/2) at Q (0,3) is

A:

Q: The directional derivative of f(x, y) = 2e* cos y at (0, ) in the direction of v = (-6, 8) is

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Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: Find the derivative of f at point P in the direction of u. f(x, y, z) = 6x² + 2y – 7z?, P = (8,–6,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

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 directional derivative of the function f(x,y) = y² Inx at the point (1,2) in the direction…

A: Given function, f(x,y)=y2 ln x Point 1,2 and vector u=3,4 The unit vector of u is…

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

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

A:

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

A: Gradient problem....

Q: What is the derivative of f(x,y) y° at P = (3, 1) in the direction toward %3D Q = (4, –3)?

A:

Q: The directional derivative of f(x, y) = xe + 2y at point (2, 0) in the direction of the angle = is:…

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

A: Given function and point is

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

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Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

A:

Q: The directional derivative of f(x, y) = -e" cos y at (0, ) in the direction of v = (-6,8) is

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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: Let f(x, y) = xe". What is the maximum rate of change of f at the point (2,0)?

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Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y) - - 3ху + 5y, Po(1, - 5), А-…

A: We have to find the directional derivative of the function P at (1,-5).

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: Let f (z) = (7z + 9) (i – z). What is the real part of the derivative f' (1+ i)?

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Q: The directional derivative of f(x, y) at the point (a, b) in the positive y- direction is f (a, b).…

A: Solution: We know that if f(x,y) is a function of two variables x and y, then fx at a point (a,b)…

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: Evaluate the derivative, where r1(t) = (t, t³, tª), r(2) = (0, 4, 5), and r'(2) = (3, 1, 2). (r(e) ·…

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

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Q: Let f(z, y) = ze. What is the maximum rate of change of fat the point (2,0)?

A:

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: vy B. Find the derivative of function f(x, y, z) = 3e* cosxy + ex² + Inzx at point P(1,0,) in the…

A:

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find the Partial derivative of f with respect to y for * f (x, y) = x+y

A: →While calculating ∂f(x,y)∂y , consider 'x' as constant.→∂∂yuv = v∂u∂y-u∂v∂yv2

Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

A:

Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Q: Find the directional derivative of the function at P in the direction of v. f (x, y) = 3x – 4cy+ 9y,…

A: