Find the derivative of the given function at the point (a, a?, a) in the direction of w = ai + 2aj + 2ak. y2 Vx2 + 3z² 8a3 p(x, y, z) = 8aVx2 + 2y + z2 + %3D a2

Q: QY Find the direction derivative of f(xg)=Xxy at the paint (2,1),by the diretion of v - i-j

A: Solution:-

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: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Q4/(A) Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction.

A: The given function is fx,y=xey+cosxy at the point 2,0. Find the derivative of the function. Here we…

Q: (a) Find the derivative of f(x, y, z) =x²- xy²- z at Po(5, 1, 0) in the direction of v=2i-3j+ 24k.…

A: Given: f(x, y, z) = x2 - xy2 - z, P0(5, 1, 0) and v=2i - 3j + 24k.

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2x2 + y2, P0(-1, 1), u =…

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Q: z = Vx4 + yf, fz (1, 2)

A:

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

A:

Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

A:

Q: a) Find2 of the function y = dy 2 %3D dx cotx cotx b) What is the derivative at x = onk 4.

A: 1/CotX = tanX.

Q: 2. Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1,1) in the direction…

A:

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 =…

A:

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

A:

Q: Find the derivative of the function at Po in the direction of A. 1- f(x, y) = 2xy - 3y² , Po ( 5,5),…

A: As per our guideline we are supposed to answer only one question you can repost other in next…

Q: Q2// A) Derivative following functions by using chain rule m 1) y = Vu, 2) y = 4u, -Va+1 Vx+1

A:

Q: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

A: We have given function fx,y,z=x3-xy2-z, point P01,1,0 and vector v=2i^-3j^+6k^

Q: calculate the derivative indicated r,(0), r(t) = (e2t, e−4t2, e6t)

A: It is given that, rt=e2t,e-4t2,e6t. Note that, If  rt=ft,gt,ht where f, g and h are differentiable…

Q: Find the derivative of the function at Po in the direction of A g(x, y) = x - (y/x) + V3 sec (2ry),…

A: Let us consider the given function z=f(x,y) The directional derivative of the function at Point P in…

Q: Find the derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy + 3y², Po(4, - 2),…

A:

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: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y²/x) + V3 sec-1…

A:

Q: Consider the function f (x, y) = x²y³ – 3xy³. Compute the value of the derivative frvy at the point…

A: Given function is f(x,y) =  x2y3 - 3xy3 we have to find fxyy at the point (2,1).

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 u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

A:

Q: Q2: Find the derivative of f(z,x) = xe* + cos(2zx?) at a point (0,2,1)in the direction of V = i - 3j…

A:

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 ?

A:

Q: Find the directional derivative of f(x, y) = Vxy at P(9, 1) in the direction from P to Q(12, -3).…

A: Given that: f(x,y)=xy        at P(9,1) in the direction of Q(12,-3)

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

A:

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

A:

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

A:

Q: Find the derivative of f at point P in the direction of ủ. f(x, y, z) = 3a? + 8y² – 42², P = (9,2,…

A:

Q: The directional derivative of f(x, y) = e cos y at (0, ) in the direction of v = (-6, 8) is -7 5/2…

A: Explanation of the answer is as follows

Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 6x+10y,…

A:

Q: 4. y2 +2xy 4, find y" Ans. y" = (x+y)

A:

Q: The derivative of ƒ(x, y) at P0(1, 2) in the direction of i + j is 2sqrt(2) and in the direction of…

A:

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: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

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 y with respect to x in the f a) y = u u +1 and u= 3x - 2 b) y=Vu + 2u and u=…

A:

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

A:

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 the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

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

A: Find the total derivative

Q: Find the derivative, or y', of ³ – Vy = ¿y² + 6 at (2,1).

A:

Q: Find the derivative of the function at the given point in the direction of A. f(x, y, z) = tan-1 8x…

A: Here we have to find the directional derivative of f(x,y,z)=tan-18x3y+8z at a point (3,0,0), in the…

Q: find the directional derivative of f (X, 4) = 3x² + 5y² at the poin t (1,-1) in the dccection of V…

A:

Q: Find the derivative of the function f(x, y) = x²y – 4y3 at the point Po(2, 1) in the direction of v…

A: The given function is:  f(x,y) = x2y - 4y3