find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v = 4i + 3j

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: Find the derivatives of the functions in Exercise y = (1 + t^2) cot-1 2t

A: The given function is y=1+t2cot-12t.

Q: Find the derivative of the function at P, in the direction of u. 2х- у g(x,y) = 5xy + 6' Po(1, - 1),…

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Q: Find the derivative of the function f(x.y) =x² +xy +y° at the point (7,8) in the direction in which…

A: Introduction: For a multi-valued function, the gradient is the vector that is directed towards the…

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: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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

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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 the function. z = (4 – t)(1 + t?) `

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Q: Find the derivative of y with respect to x if y = (13x - 26x+26) e -8x y =D %3D

A: Explanation of the answer is as follows

Q: Find the derivative of y with respect to x in the following equation y = 1¹ where u = 1-z O x² O-x²…

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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: 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 (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

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 y with respect to x, t, or u,as appropriate.55. y = ln (cos^2 u) 56. y = ln…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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

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

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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: Obtain the derivative of the function y y = (e*1) (In(2cos(x² – 4x))

A: The given function is: y=e3x+1ln2cosx2-4x

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: 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=1/b²[a+bx-aln(a+bx) where a and b are constants

A: Derivative of function

Q: Find the derivative, dy/dx of the following using the chain rule: a) y= . . x+1 d) y= 3x+1" f)…

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Q: Vw Find the derivative of y = 3W with respect to w. dy dw

A: To find dy/dw

Q: A. Find the derivative of the function at o P in the direction of A f(x, y) = x V3sec-1(2xy)at P.…

A: To find the derivative of given function means we have to find the directional derivative of the…

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: Find the derivative, dy/dx of the following using the chain rule: a) y = 3. 'x+1 b) y = ()³ 5x+1 %3D…

A: As per guidelines we can solve only one question at a time so if you need more answers kindly repost…

Q: Find the directional derivative of the function f(x,y) = 3-6xy+ 10y at the 1 point P (1,5) in the…

A: The given function is fx,y=3x-6xy+10y . Obtain ∇fx,y as follows.…

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=…

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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: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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

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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 all second order derivatives for the following functions. (a) f(x, y) = 2² +3ry+2y², (b) f(x,…

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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 derivative of y with respect to v. y=v1-v2 +5 cos - 1, y = dy dv II

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Q: The derivative of the function y = cos VI at z = is equal to 4

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

A: Derivative of a function f(x,y)  at (x0,y0) in the direction of a unit vector u^=ai + bj is ,…

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: A. Find the derivative of the function at o P in the direction of A f(x, y) = x – E) V3sec-1(2xy)at…

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Q: - 18x Find the derivative of y with respect to x if y = e dy %3D dx

A: We have to find the derivative

Q: Find the derivative of y with respect to x. y = tan -1V3x O A. V1- 3x 1 O B. 2(1 + 3x)/3x 3 Oc.…

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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