Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges V12 sin(x – 2y) + 8y² – x³ – 6x²y + 32)

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

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A: Differentiate the function with respect to x.

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Q: Find the particular anti derivative that satisfies the following conditions: dy/dx=3x+5/sqrt3 of x ;…

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Q: Find the directional derivative of Du" f (2,1) in the direction of: å = 31 + 4j f(x,y) = INGE12…

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Q: Find dy/dx by implicit differentiation. (a) Vry = x- 2y +1 (b) y³e2 + 53y = sec(3x)) (:) (b) x = In…

A: To find the implicit differentiation.  We use the , basic product and chain rule of differentiation.…

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A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: If f(x,y) = ln(xy) + x2y2, in what directions is the second directional derivative of f(1,1) = 3?

A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

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Q: Find the differential dy of the given function. (Use "dx" for d> y = 8x² – 4 dy = %3D

A: Formula :

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 dz/dr if z as a two variables function in r and y is defined implicitly by y3 + x22 + r sin r…

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Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

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Q: Find the directional derivative of the function f(x, y, z) = 3e" sin(xy) in the direction of v = 3i…

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Q: 1 -dt = xy ndif y + J sint+1 secx dx

A: Since you are asking multiple questions. As per our guidelines, we are supposed to answer only one…

Q: : Find the derivative of f(y, z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i – 3j…

A: This is directional derivative, just write the formula and solve accordingly.

Q: Write the differential dw in terms of the differentials of the independent variables. w f(x,y,z)-…

A: To calculate the total differential dw for the given function of three independent variables

Q: Find dw/dt at t=0 for the function w=sin(x),cos(y),ln(z). Where x=-7t^2+9t+pi/2, y=t,z=e^-6t

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Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: To find the antiderivative of the below derivative

Q: Find the equation of the tangent line for f(x) = 6 tan(x) at a = %3D a) Oy = 6/3 (z -) + + 12 b) Oy…

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Q: |dx + N(x,y)dy = 0 x² + y,

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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 linear approximation of the given function at (0, 0). f(x,y) = sqrt(y+(cos(x))^2)

A: The given function fx, y=y+cos2x The linear approximation in 2 variables is given by Lx, y-fa,…

Q: Q2: Find the derivative of f(y,z) = ze2y + cos(2zy) at ppoint (9,1,0)in the direction of V = 2i - 3j…

A: The given function is: f(y,z)=ze2y+cos(2zy)

Q: Find the potential P(x,y) attached to the exact ODE 2x sin(y) +x² cos(y) y' = 0

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Q: Let y = tan(3r + 4). Find the differential dy when z = 2 and dr 0.1 %3D Find the differential dy…

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Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: dw where w = cos 8x sin 4y, x = dt and y =t". 4 Use the Chain Rule to find

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Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Let y = f(x), where   f(x) = 4x2 + 6.   Find the differential of the function.   dy =?

A: Given: y=fx=4x2+6 now differentiating given function with respect to x

Q: Q6:- Show that R = (sin t)i + (cos t)j + v3k has a constant length. And R(t) is orthogonal to its…

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

Q: Suppose that y is a differentiable function of x and w = cos(y5). Express the derivative of w with…

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Q: Compute the derivative for r(t) = (cos(8t))i + (sin°(t))j + (tan(6t))k. %3D dr dt

A: Given

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

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Q: Let f(x,y) = 8x + 10y with x(t) = cos t, and y(t) = sin t. Find the derivative of w = f(x,y) with…

A: Here we have to find the derivative of w with respect to t.

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: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

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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: Q2) A) Verify that wxy = Wyx for w = x sin y + y sin x+ xy. B) Show that f(x, y) = e-y cos 2x…

A: Here we have to find the partial derivative of the functions with respect to x and y seperately…

Q: Find the differential dy of the function y=(cos(x))(7x) a. dy=-7x(sin(7x))dx b. dy=(-cos(x))(7x)dx…

A: To Find the differential dy of the function y=(cos(x))(7x)

Q: Show that r = (sin t)i + (cos t)j + V3k has a constant length. And r(t) is orthogonal to it's…

A: Note: We are supposed to answer only one question. Kindly repost other questions as to the next…

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: Given that x'+3xy-y' = 6. Compute dy in terms of x and y by using implicit dx (c) differentiation.

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