Suppose that z is a differentiable function of x and y with dz (3, 6) дх dz = 36 and (3, 6) = 2. ду If x = x(t) and y = y(t) are differentiable functions of t with x(0) = 3, y(0) = 6,x (0) 1 and 9' (under composition) z' (0) 10, find y' (0). %D y' (0) =

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

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Q: az Find if yz – In z = x + y ax

A: To find: The partial derivative ∂z∂x, if yz-ln z=x+y. Calculation: The partial derivative ∂z∂x can…

Q: The value of local acceleration in the x direction for flOW with all wrong u = 2(1 + t) is given by…

A: Given that  u=2(1+t)  To find the local acceleration in the x direction of flow

Q: Find the indicated partial derivative. f(r, y, :) = e"vz*; fzyz fxyz(x, Y, z) =

A: Given: f(x,y,z)=exyz3 To find: fxyz=?   Required formulas: Power rule: ddxxn=nxn-1 Product rule:…

Q: Find partial derivative føyz of the function f(x, Y, z) = z ln x + 2y

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Q: If U = lx+my,v=mx-ly then prove that partial derivative of x

A: Given: u=lx+my v=mx-ly   To show: ux=-vy and uy=vx

Q: Find the indicated partial derivative. f(x, y, z)=euz²; fzyz fxyz(x, y, z) =

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Q: Use differentials to estimate the change in f (x, y, z) = x² In(5yz + 1) as (x, y, z) changes from…

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Q: a?f (or and y. that is, f(x,y) = e² with respect to ayax axay Calculate the second-order partial…

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Q: Find partial derivatives of  hxx ( x,y) , hxy(x,y), hyy (x,y)  For function  h(x,y)= ln ( x^3 +…

A: Given, h(x,y)=ln(x3+y3)

Q: Find the value of ∂z/∂x at the point (1, 1, 1) if the equation xy + z3x - 2yz = 0 defines z as a…

A: Given, the equation xy + z3x – 2yz = 0, defines z as a function of two independent variables x and y…

Q: (b) A bounded, 3B > 0 such that |f(x)| < B Vx € (0,1), continuous function on (0,1) with unbounded…

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Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

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Q: Find the value of at the point (1,1,1) if the equation 3xy +z°x-2yz = 2 defines z as a function of…

A: First do the partial differential in both the sides and then separate ∂z∂x and then put the value…

Q: Find the partial derivative at point(u,v)=(-4,0) of w=ln(xa+yb+za),x=uevsin u y=uevcos u, z=uev,…

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Q: For the function f(x, y) = Vx³ + y³ find both partial derivatives at the point (0,0) (separate by…

A: Given function, f(x,y)=x3+y33

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x?y - 4xyz + 8yz? %3!…

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Q: Find the first partial derivatives with respect to x, y, and z. fx, у, 2) %3 4x?у - 2хуz + бу2?…

A: Given  f(x, y, z) = 4x2y - 2xyz + 6yz2

Q: Find the Partial Derivatives of the functions with respect to each variable 4) f(x,y) x+ y Ans. 5,-…

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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Q: Let z = z(x, y) be a continuous function of x and y defined implicitly by In(3æ* + 4y* + zyz*) = =…

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Q: Suppose that the partial derivatives of a function ƒ(x, y, z) at points on the helix x = cos t, y =…

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Q: Find ôw/ðs and ôw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s + t, y…

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Q: The coordinates of a particle in the metric xy-plane are differentiable functions of time t with…

A: The distance of a point (x,y) and the origin is calculated by d=x2+y2 Given rate of change is,…

Q: Find the value of at the point (1, 1, 1) if the equation xy+ z°x – 2yz = 0 defines z as a function…

A: Given equation, xy+z3x-2yz=0

Q: ih fcuv,w) and its partial derivatives with respect tou and v and w and are Continous that usx-, V=…

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 10yz²…

A: As we know that f=f(x,y,z)then fx(x,y,z)=∂f(x,y,z)∂x, fy(x,y,z)=∂f(x,y,z)∂y,  fz(x,y,z)=∂f(x,y,z)∂z

Q: 8. Find the indicated partial derivative f(x, y,z) = ye + ze' + xe; f(x, y,z)

A: Partial derivative of the function

Q: Find the 1st order partial derivative of f(x,y,z) = 4x^3y^2 - e^zy^4 + (z^3/x^2) + 4y - x^16

A: The given function is f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16.

Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

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Q: 46. s(х, у) tan (y/x) -1 =

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Q: Find the rate of change of f (x, y, z) = 3xyz in the direction normal to the surface yx² + xy² + yz²…

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Q: Q4) If Z-y , Determine the first order partial derivative (w.r.t, x) and (w.r.t, y)

A: To find: The first order partial derivative of Z=yx2 with respect to x and y. Concept used: The…

Q: Differentiate implicitly to find the first partial derivatives of z. 2x? + 5y2 + 11z² = 81 %3D az ax…

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Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

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Q: Find the value of at the point (1, 3, 1) if the equation 6xz + ylnx – 5x² – 1 = 0 defines x as a…

A: Given equation is, where x is a function of two independent variables y and z and the partial…

Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

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Q: Show that the differential form in the integral is exact. Th (1,2,3) | 2xy dx + (x² -z°) dy -6yz dz…

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Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

A: Given: (x,y,z)=(1,1,1) and z=6xy+z4x-2yz-5=0

Q: Find partial derivative of: z=f(x,y)= e^x^2+y^2  +   cos(x+y^2

A: For this question of partial derivative we need to find out first derivative with respect to x and y…

Q: Find ôw/as and ôw/ôt using the appropriate Chain Rule. Function Values w = sin(7x + 8y) X = s + t, y…

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Q: dz Suppose that z = f(x, y) is differentiable at the point (8, 16) with f,(8, 16) = 3 and f, (8, 16)…

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Q: 4. Use the limit definition of partial derivative to find f, (x, y) and f, (x, y). a) f(x,y)=/x+y

A: As per our guidelines we are supposed to answer only one question i.e. the first question. For the…

Q: /alue of divergence of function (x2y2)î - (z³y – 4x) ĵ + 4y2 xk at (1, 2, 1) is

A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

Q: Calculate fz(2, 3, 1), where f(x, y, z) = xyz.

A: Given,          fx,y,z=xyz

Q: Calculate the partial derivative f(5, 2, 5), where f (x, y, z) = xyz.

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Q: Find the indicated partial derivatives. f(x, y, z) = cos(5x + 7y + 3z); fxyzı fyzz 50 sin (5x + 7y +…

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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Q: 8. Find the indicated partial derivative f(x, y,z) ye" + ze" + xe; f (x, y,.z)

A: Partial derivative