Let f(r, y) = x sin ry. Fi (a) fz(x,y) (b) fy(r, y) Sy(x, y) (c) fyy(", y) YY (d) fyr(r, y)

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: The maximum directional derivative of f (x, y, z) =r sin(zy)-yz + 10 %3D at (1, -1, 0) is O v3 O 2…

A: For the scalar function f(x,y,z), gradient is the maximum rate of change.  So, first we will find…

Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

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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: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

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Q: Calculate the directional derivative of the function f(x, y, z) = 2x³y − ln(y)x²z − z² at the…

A: Answer

Q: If f(z, v) – 4z°y+ 8zy, then the total differential of f at z-1 and y - 1is: O df - 17 dz + 22 dy O…

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Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: Let f(x, y, z) = 3xz + sin(ry)e*. what is faz? Find the gradient at the point (0, 0, 0)?

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture then an…

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: Find f-(x, y) and fy(x, y). f(z, y) = (y° tan(5z)) f-(x, y) fy(x, y) =

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Q: 2, 0 1

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Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

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Q: Find the directional derivative of f(x, y, z) = cz+y² at (1, 0, 4) in the direction of a =. = IZ

A: Differential equations are those equations of mathematics that involve dependent variables ,…

Q: f(x, y, z) dx dz dy f(x, y, z) dy dx dz f(x, y, z) dy dz dx

A: Given ∫064∫x8∫08-yfx,y,zdzdydx So, limits of x from 0 to 64 limit of y is from  x to 8  limit of z…

Q: Find f. fy for f(x,y) = xcosy + %3D x5 siny3 ey

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Q: Find the directional derivative of f(x, y, z) = x²y + y²z v = at P(1,2,3) in the direction of %3|

A: In geometry and physics and its engineering applications, we use two kinds of quantities, scalars,…

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: f(x, Y, z) =

A: We are asked to find the gradient of the function.

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: 2. Prove that the directional derivative of f (x, y, z) = xy sin z at direction v = i+2j+ 2k is .…

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Q: f(r, y, z) = byz In(4ry) %3D fz = fy = た=

A: Given:

Q: Find dy or y' using implicit differentiation. r'y-y= Oy 1- 3r'y %3D Oy = 1 3z'y 3z'3y 1 %3D 1 3z'y…

A: The given equation is x3y3-y=x

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

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Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

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Q: Consider h(x, y, z) = cos (xy) + eyz + ln (xz). Determine the directional derivative of h at the…

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Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

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Q: Let f(x, y) = xcosy- y e*y. fxy at (1,0)is equal to:

A: For finding the Partial differentiation we need to take one variable constant and differentiate the…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given:        fx,y,z=xy sinz         x,y,z=1,2,π2    direction v=i+2j+2k   Differentiate the…

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(z)with Im(f(z)) =v(x, y).

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Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

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Q: The directional derivative of f(x, y) = cos(x²y³ ) in the direction of the vecto v = 3i + 4j is Du…

A: The given function is: f(x,y)=cos(x2y3) So, ∇f(x,y)=∂f∂x,∂f∂y…

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

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: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y).

A: using CR equation we get....

Q: Find fa, fy, and fz. f (x, y, z) = z In(xʻy° cos(52)) 4,3 COS x*Y fn = fy = fz =

A: Please refer the attached image for complete solution.

Q: Find the directional derivative of f(x, y, z) = xy² + yz% at P(1, – 1, 1) in the direction of a = i…

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Q: Find a potential function for F(x, y, z) = (y² cos z, 2xy cos z, –ry² sin z). %3D COS

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Q: Obtain tne general voluti on' 1. (xy + x) dx (x*y* + x * + y² + ) 2 2 %3D X cos²y dx =tany dy 2 Q.…

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: prove that x^2y/(x^2+y^2) is not differentiable at 0,0 when  x^2y/(x^2+y^2) if (x,y) not equal to…

A: f(h,k)-f(0,0) =hfx(0,0) +kfy(0,0) +h2+k2∅(h,k) h2kh2+k2-0 =hA+kB+h2+k2ϕh,k ...(1) A =fx(0,0)…

Q: Find the first partlal derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 9yz? %3D…

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Q: Let x and y be differentiable functions of t, and lets = √(x2 + y2) be the distance between the…

A: Given equation is s=x2+y2. Compute the derivative of s with respect to t.…

Q: If (x, y, z) = cos(x – y)+ e² compute directional derivative of Í at (3, 3, 0) in the direction of ŷ…

A: Option C is correct option.

Q: Find of /dy if f(x, y) = y sin(xy) 1 + xycos(xy)csc(xy) csc(xy) B) xy cos(xy) + sin(x) A) O

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Q: Find fr and fy- f(x, y) = ets dt %3D f (x, y) = %3D fy(r, y) =

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