Find an equation of the tangent plane to the given surface at the specified point: xy2 = yz? – 3z – xyz, (0,3,1)

Q: In explicit method of hyperbolic PDES, the second initial condition, the one involving g, gives…

A: Given,

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: use implicit differentiation to find dy/dxin terms of x and y .

A: We have to find implicit derivative (dy/dx) of the curve .Information is given below:

Q: a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and…

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Q: Find a function w = ƒ(x, y) whose first partial derivatives are ∂w/∂x = 1 + ex cos y and ∂w/∂y = 2y…

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Q: Use implicit partial differentiation to find at (-2,3,2) if x? +y +z = 2yz-6xy+1. %3D

A: The given function is: x2+y2+z2=2yz-6xy+1

Q: dz at the point (1,1,1) if the equation 4xy +z°x-2yz = 3 defines z as a function of the two…

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Q: (a) Find the partial derivative of f with respect to x. fx(x, y) = (b) Find the partial derivative…

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Q: Find all second order partial derivative with respect to variable x and y. F(x,y)= x cosxy + y sinx…

A: We have to find all second order partial derivative with respect to variable x and y: Given:

Q: Please show your answers to at least 4 decimal places. Suppose that f(x, y) = x'y". The directional…

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: Please only compute this: Fxy  What is the sign of the partial derivative? (Positive, negative,…

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Q: ди Calculate the partial derivative using implicit differentiation of + y = 6 at (x, y, w) = (1,2,…

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Q: w = xy +z+ sin(x + yz)

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Q: The temperature of a solid is given by the function B(x, y,2) =x*y: +4x, where x, y, z are space…

A: Given temperature function Bx,y,z=xy+4x, given point P1,-2,1, and the direction a=2i-2j+k. Therefore…

Q: Find the first partial derivatives with respect to x, y, and z. Ex, y, 2) = 3x?y - 6xyz + Byz? ,(X,…

A: We have to solve this problem by partial derivative method.

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: Give 1 problem of partial differentiation of function of U with respect to 3 independent variables…

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Q: Find the partial derivative of f(x,y) with respect to y at the point (3,2) f(x,y) = ln(x^2y-xy^2)

A: A partial derivative of a function of several variables is its derivative with respect to one of…

Q: Find all first and second partial derivatives of f(x, y) = sin(ry)

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Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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Q: f(x, y) = ex + tan(x + y2).

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Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1, 1) in the direction of from…

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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: Calculate the partial derivative using implicit differentiation of x° w + w® + wz² + 3yz = 0. ди dz…

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: Let f(x, y) sin r + sin y + sin(r+ y) for 0 <I<5, 0 < y < T. Find the critical points then classify…

A: If its sinx+siny+sin(x+y) Let f(x,y)=sinx+siny+sin(x+y) We havefx=cosx+cos(x + y) y=cosy+cos(x+y)…

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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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: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

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Q: (a) Find the tangent plane and normal line of the surface f(x, y, z) = x3 + y² – 6z + 5 = 0, at the…

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Q: What is the result of the partial derivative 3(z² + y sin (z)) Select one: a. 2a + y * cos(x)

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Q: If we discuss the derivative of the function f(z) = z. Imz by Cauchy- Riemann equations. we see fz)…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the indicated partial derivative.

A: Given that, f(x, y) = y sin-1 (x, y) We have to find fy(1, 1/2).

Q: I. Consider the function g defined by 1 g(x, y) : = cos (Tx ) + log3(x – y) In what direction does g…

A: The given function is gx,y=cosπxy+1log3x-y

Q: The maximum directional derivative of f (x, y, z) = x² sin(zy) – yx + 10 | at (-1, 2, 0) is

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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: v = exy In(x +y)

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Q: but its partial derivatives are not continuous at (0,0).

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Q: Calculate the partial derivative f2(3,3,1), where f(x, y, z) = xyz. %3D

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Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: dg Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7 where g(x, y)…

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Q: 1.(i) Suppose U (x, y) = 4x² +3y². Calculate aU/ax and JU/ay and evaluate these partial derivatives…

A: In this question we have to find δUδx and δUδy and we have to evaluate partial derivatives at x=1…

Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Let f(x, y) be a function whose partial derivatives exist and are continuous at a point (a, b).…

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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: Please show your answer to at least 4 decimal places. Determine the gradient of f(r, y) = e sin(4y)…

A: The gradient is just the vector of partial derivatives.

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: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives