Ql: f(x.y)-y cos xy over the rectangle 0sxs , 0 sys1

Q: xp %3D 0. dy %3D 18 + 9t2 dt xp for y = Find ||

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Q: dw Find if w = xy + z,x = cost, y sint and z =t at t = 0. dt

A: In the given question, the concept of the derivative is applied. Derivative We can use a derivative…

Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: Q1-lf x= cot-VE, y= , find dy dx' dx2 at t = 2. t+1

A: We have to find first order and second order derivative of the given parametric functions.

Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: Find dy at (x, y) = (TT, T) for sin (xty) = 2x-ay %3D dx

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Q: dz 2. Given z = 4x2 + y²,x = sin t, y = t², find- %3D dt

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Q: (b) cos(x² + y²) dy dx where R is the region 9 < x² + y? < 49.

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Q: Solve the I.V.P using [x = zry]. y di dx + (y cos ( 1 ) - x) dy = 0, y (0) = 262

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Q: dw w=x +y, x-cos r, y-sin/ ise dt Irm

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Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: Compute f cos(Tæ) dæ + 10xy dy, where y is a part of parabola y = 3x? from the point (0,0) to the…

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Q: dz Given z = 4x2 + y²,x = sin t, y = t2, find : dt

A: Topic = Derivative

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 fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: |dx + N(x,y)dy = 0 x² + y,

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Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

Q: Find: Jy (完)。 (2) X. dz W=X+y - そ + Sin Z

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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: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: find dy/dt y=cos^2(cot^7t)

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Q: Is f(x, y) = sin?(xy²) a solution to the PDE sin(xy²) > 0? Je * Je ax ;= (2x + y)(2y) cos(xy²)/F…

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Q: Q3) For f(x,y) = Sin(x,y) find fryxy at (1,–). %3D

A: Given query is to perform indicated derivative operation.

Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

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Q: Find the differential dy. (a) y = xv8- x %3D dy %3D (b) y = (1+ x)7 dy

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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: j.x'y-y' sin 2x In x+ y

A: Using implicit differentiation rule of derivative,

Q: f x = sec(z) and y = tan(z) , then dy at z = dx 4

A: We can use the chain rule of derivative in order to solve the given problem.

Q: of and dy For the function f(x.y) = sin (2x - 5y), find dx of of

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Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: (e* – sin y) dx + cos y dy = 0; when x = 0,y = 1 - %3D

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Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: dz Given z = 4x? + y²,x = sin t, y = t², find - dt

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Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: Integrate f(x, y)= y cos xy over the rectangular 0 sxsm, 0 s ys 1*

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Q: find the dy リ=(メ+z)mx, (xを when 3In X

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Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: Scy dx –x dy; C is the cardioid r=1- cos 0.

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Q: Find fr and fy- f (x, y) = 8e dt

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: %3D a) Find fyxyx for f(x,y) = In(xy) – cos (xy) at (1,t).

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Q: dy Find -5 y%3D(2+cos4t) dy dt

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Q: Consider z = x² + 3y², where x = sin t and y = cos t. Calculate dz / dt.

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Q: dv dv If V = ÷f(0) and x = r · cos 0 , y = r · sin 0 . Prove that x -+y÷= -V dr dy

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Q: Q2 Find (d y/d x)& (dy/dx?) y 1/ cos xy ex %3D

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Q: Find dy/dt. y = cos(~/4t + 11) %3D

A: The given equation is, y=cos4t+11 So, the derivative of the given function is:…