Find f, and f, and evaluate each at the given point. y' f(x, y) = arctan (-) (4, -4) fx(X, y) = fy(x, y) = f,(4, -4) = fy(4,-4) = |

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Q: 23. Evaluate Jcxy dx + (x + y) dy along the curve y = x² from (-1, 1) to (2, 4).

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Q: Let f(x, y) = sin(3x + 5y) and P = 3 Find the maximum rate of change of the fucntion f at the point…

A: Find gradient of f(x,y). Find compute the point . Take the magnitude of the same .

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

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Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

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Q: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

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A: It is given that,

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Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: If Z= x³ +y* +(x sin y) + (y cos x), Find (Zxx+ Zyy=?)

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Q: Find the length of the curve f(x) = ln(sin x), 0 ≤x ≤π/6.

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Q: Find dy if arctan(x + y) = xy-

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Q: Find dy/dx in terms of x and y if arctan (x^3)=xy^3?

A: To find the derivative of the given function.

Q: Where is the function f(x, y) = e' arctan (VI+In(x+y)

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Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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Q: Find fa, fus and fz. f (x, y, z) = (5z)) 3z In (x*y cos

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Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Express in form y=f(x) by eleminating the parameter x = ln t , y = 2 − t

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Q: Find In(y') at the point (0, 1/e) where xy° – In(xª + y) = 1.

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Q: Find the equation of the tangent line to the graph of F(r)= 2z²+2r+1 evi dy at r 0. sech z

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Q: Express x = ln(7t), y = 9-t in the form y = f(x) by eliminating the parameter.

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Q: Compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dy. C is a unit circle with counterclockwise…

A: We need to compute ∫C(ln(x + 5) - x2y)dx + (xy2 + sin(ey))dywhere c is a unit circle Equation of…

Q: The function f has a continuous derivative. If f (0) = 1, f (2) = 5, and f (x) dz 7, what is %3D %3D…

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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: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

A: Find the equation of the tangent plane to z = ln(2x + y) at −1,3

Q: Find dy of the function y = cos2 3X + √√Sin x dx

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Q: y' – ey : = sin x

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Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: Find dz/dy of z=arctan (x/y)

A: The given function is z=tan-1xy.

Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

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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: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Find dz/ðx , dz/ðy at the point (1,1,1) if x³ + z² + ye + xz cos y = 0

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Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: Suppose F(x, y) = 0 and y is a differentiable function of x. Explain how to find dy/dx.

A: It is given that F(x, y) = 0 and y is a differentiable function of x . For the function F(x, y) = 0…

Q: implicitly dx

A: Solved below

Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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