Find the derivative of the function at P, in the direction of A. f(x,y) = 4xy + 2y, Po(4, - 4), A = - 5i – 6j

Q: Find the derivative of the function at P0 in the direction of u. f(x, y) = ln(-9x - 4y), P 0(4,…

A: use gradient for finding the directional derivative.

Q: Calculate the derivative of the function xe" at the point x = 0 %3D O 1 e O 2e

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Q: - 9x Find the derivative of y with respect to x if y = e dy %3D dx

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Q: Find the derivative of the function at P in the direction of A g(x, y) = x - (v² /x)+ /3 sec*(2xy),…

A: To find: The derivative of the function at P0=1,1 in the direction of  A=12i+5j Given information:…

Q: Find the derivative with respect to x of the function r4x t² F(x) = e dt.

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Q: Find the derivative of y with respect to x if y = 4Vx(2x + 3). D. E - А. 6(2x+1) 3 B. C. 12V1 + 6 O…

A: Given: y=4x2x+3 ⇒y=8x32+12x12 Since, we know that ddxxn=nxn-1

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: Find the derivative, dy / dx, at the points where x = 1 on the folium                    (x 2 + y 2)…

A: given,       (x 2 + y 2) 2 = (25/4) x y 2 .

Q: Evaluate the derivative of the function r(t)=⟨lnt,3t+1,t2⟩ at t=1.

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Q: Find the derivative of the function at P, in the direction of g(x,y) = x - (v² /x)+ /3 sec*(2xy),…

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

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

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

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Q: + (z), V1– 2z y =1- cos (z) + /1 – 2z

A: Given : y = xcos-1x+1-2x

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 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: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 3x-2 1. Z=. ;d'z/dx? (x-1)2 2. Y= (2 – x³ )5…

A: Given: 1. z=3x-2x-122. y=2-x353. y=2x+125

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

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Q: Find the derivative of y with respect to x. 8x y = tan 3 - 24 O A. 64x2 + 9 O B. 64x2 + 9 24 Oc.…

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Q: f(x, y) = e²+y² = e&+y?

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Q: Find the derivative of this complex function: where z=x+jy (2+jj?

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Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y 2xe X- 2e X O 2xeX O 2xeX +…

A: Finding the derivative

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…

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Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: Find the derivative of f(x, y) = xe + cos(xy) at the point (2,0) in the direction of v=3i-4j. B) 5 O…

A: Please find the answer in next step

Q: Find the derivative of the function f(x, y) x² + xy +y2 at the point (6, 7) in the direction in…

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Q: Find the derivative of the functions below: Rw) = x In(e f'(x) = a) f(x) = In(3x) f'(x) = b).

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Q: find the derivative of y with respect to x, t, or u,as appropriate. y = e^(cos t + ln t)           .…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: find the partial derivative of the function with respectto each variable. g(r, θ) = r cos θ + r sin…

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Q: 2) Find the derivative of the function. T(r) = ar² + 2e" + n². %3D

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Q: Find the derivative of the function using the definition of derivative. dy Ay lim dx A-0 Ar 1. y=37…

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Q: Find the derivative of y with respect to x in the following function at (1, 1/3) u? y = u' +1 and u…

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Q: Find the derivative of the function f(x, y)=9x² +6y at the point (6,-3) in the direction of v = 3i –…

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Q: D-the derivative is y = In In (VW) 1 +

A: The objective of the question is determine the derivative of the given function.

Q: Find the derivative of the given functions. 1. D,(x²cos 2x) 1 1 2. y=x+zsin 2x 3. f(x)= sin?(5x + 4)

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Q: Calculate the derivative of y with respect to x, if x^4y+4xy^4 =x+y. dy/dx =

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Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

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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: I. Find the derivative of y with respect to x. Use the given relation in its implicit form. d?u 3.…

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Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

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Q: Find the derivative of the function. -6x - 2 e** y =x e dy %3D dx II

A: Topic = Derivative

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 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: Find the derivative of the function. y = In) x +6. (a)"* g(x) = log,(x) 9'(x) = (b) y = x5x + 2 (c)

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Q: Find the derivative of the function at the given point in the direction of A. f(x.y) = 7x + 8y.…

A: Directional derivative: - The partial derivatives of f give the slopes ∂f∂x in the positive…

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

A: Find the total derivative

Q: Find the derivative of f(x,y) = xe² +cos(xy) at the point (2,0) in the direction of V = 3i – 4 j .

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivative of y with respect to x. y = sin -1(et) OA. 5e 5t /1- e 10t O B. - 5 e 5t /1- e…

A: We have to find

Q: Find the third derivative of f (z) = T2x +I. fll! (z) =

A: Explanation of the answer is as follows