Q.3 Let f(x, y,z) = y+ y² tan xyz Find the directional derivative Duf in the direction of u = at (1, 2, [3 M

Q: Q1// B: If u+v=e cos y and u-v=e'sin yfind the Jacobain of the a u, v at (x.y) (1,0) dx,y function

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Q: 8. The second directional derivative of a function f(r, y) is DS(x, v) = D.[D.f(r, y)]. If f(r, y) =…

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Q: Consider the function 3..2 f(x, y) = cos(rxy) – a°y?. = cos(Txy) – x°y°. a) Find the equation of the…

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Q: Match the D.E. with a direction field: y' = t+y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2 –…

A: NOTE: Horizontal axis is t-axis  .

Q: Match the D.E. with a direction field: y' = t+ y – 1, , y' = sin(t)sin(y), , y' = 2 – y, , y' = t(2…

A: NOTE: The horizontal axis is t-axis.

Q: sa (0, ") : If f(1, y) = 18e* cos z + 5 cot y, then the total differential of f at (0, O df = 18 dr…

A: Total derivative

Q: Let f(x, y, z) = x'e sin(x yz) %3D 12 find dyəzd' x at the point (2, 0,0)

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Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 23 + xe² =…

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Q: If w= y(x- mz)i + yz*j + In XZ -1 k and f-w cos (xy-x) x* + m y find at point (0,2.-m): (1) the…

A: Given - If w = yx - mzi + yz2j + lnxz - 1x2 + mk and f = w ·cos-1xy - x2yj To find - At point ( 0,…

Q: (x cos-1(yz – z²) ту? xZ – 1 n( i+ mxy²j + y(z – mx)k \z² + m/ f = w • 1) if w = Find at point (-m,…

A: w¯=lnxz-1z2+m.i^+mxy2 j^+y(z-mx).k^andf=w¯.xcos-1(yz-z2)my2 j^f=xz-1z2+m.i^+mxy2…

Q: Consider the graph of f(x, y) = excos(xy²). Find an equation of its tangent plane at (0,0, 1) and…

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Q: Q9. Find the equation of the tangent plane to f(x, y) = x ln(y) +x²y+3 at the point (x, y) = (2, 1).…

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Q: Find and by implicit differentiation, and confirm that the - dy results obtained agree with those…

A: The solution is as follows

Q: define y as a differentiable function of x,  find the value of dy/dx at the given point. 25. x2 + xy…

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Q: (a) Find the point of intersection of the tangent lines to the curve r(t) = (3 sin(at), 6 sin(At), 5…

A: Given, r(t)=3sinπt, 6sin(πt), 5cosπt Now we find its derivative, r'(t)=3πcosπt, 6πcosπt, -5πsinπt…

Q: 4. If u = xy + y²z³, where x = rset, y = rs²e-t and z = r²s sint, find the value of du/ds and au/ar…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: O A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point…

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Q: directional derivative

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Q: H.W: 1. find the derivative of the function f(x, y, z) = xy+ yz+ zx ,at the point P,(1,-1,2) in the…

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Q: Given a surface f(x,y) = -3x + (4)y². Find the derivative in the direction of v = at the point (6,…

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Q: II. Consider the function g defined by 9(z, y) = cos (7z/T) logg(z Do as indicated. In what…

A: We know that the gradient of the function g contains the two vectors, one in the direction of x-axis…

Q: 2. Let F(t) = (e' cos t) î+ (e' sin t)j+ek. a. Find symmetric equations of the line tangent to the…

A: Given:  F→t = et costi^ +et sint j^ +et k^  To Find:  Symmetric equations of the line tangent to the…

Q: 1. Consider the curve F(x, y) = 0. Show that if F has continuous second derivatives, then a formula…

A: We will use chain rule of partial derivative  If F is a function of  two independent variables x and…

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

A: We have to find the direction derivative of given function.

Q: 7. Consider the function f: R → R³ given by: t+1 f(t) = sin(cos(t)), tet) t2 +4° Find f'(t) for all…

A: The derivative of the function is the measure of how fast the function is varying with respect to…

Q: 4. Let f(x, y) = sin(x²y) + vx + e+y. Find the equation of the tangent plane to the surface z f(x,…

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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: Consider the function f: R R³ given by: t+1 f(t) = (; sin(cos(t)), tet t2 +4 Find f'(t) for all t e…

A: please see the next step for solution

Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

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Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

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Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: 5. Express the curve by an equation in x and y. x(t) = 2- sin(t) y(t) = cos(t) a. (x-2)² + y² =1 b.…

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Q: Q5.a) Find if sec?y = x? + t² dt Jsiny dx dy b) Find if tan?y = x² + Jysinx cotx VE2 +1 dt tZ+Idt

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Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

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Q: 5. Let f(1, y) = re" + cos(ry) and P: (2,0). A. Find the directional derivative of f at P in the…

A: Given information: The function is f(x,y)=xexy+cosxy and P:(2,0) and the vector is v=3i-4j. (a) To…

Q: 1. (a) Let /(r,y)- cos(z + 2y). Compte the directional derivative Da/(r.y), where u- (b) Compute ff,…

A: Given that, In part (a), f(x, y) = cos(x+2y) u=(x,y)=-12,12 We have to find the directional…

Q: i+ (x-my)j + zx*k and f=w0 0 cos "(yz - y²) xy If w In + m find at point (-m,0,2): (1) the…

A: We are provided with functions: w=lnxy-1y2+mi+zx-myj+zx2kf=w·cos-1yz-y2zk The objectives are at the…

Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: 9–18 Find the directional derivative of f at P in the direction of a. 9. f(x, y) = 4x°y²; P(2, 1); a…

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Q: 2. (a) Let z ry, r =r cost and y=r sin t. Compute by using the chain rule and express your answer in…

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Q: 5. Let u(x) be a differentiable function with u(1) = 2 and u'(1) = 3. Find an %3D equation of the…

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Consider the given function, xy+y2-3x-3=0 now differentiate with respect to x,…

Q: 3 For which values of a E R the tangent plane to the graph of f(x, y) = 1+ sin(ax + y²) at the point…

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Q: Given the curve y2º = x in the xy-plane, for what value of y, if any, does the derivative of y with…

A: Differentiation w.r.t to x

Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Suppose z is a differentiable function of x and y implicitly defined by the equation E : 2³ + xe² =…

A: Given function z3+xez=2-y3+lny3 cos(y+1)

Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: x + Y f(x, y, z) = x sin + e*% – 1

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Q: 1. Calculate the derivative dy/dx for the plane curve defined by the equations: x(t)=t²-4t,…

A: Given that: x=t2-4ty=2t3-6t