4. Let f(x, y)=2x*y' . Find f,(x,y)

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: 4. It f(x,)= (x?+Zy^)+Z and ū= a.) Find the derivative of t in the direction Of ū at 13,2) -

A:

Q: If f(x, y, z) = 16xy – 4yz – 4zx + 3, then the first order partial derivative fz = - - (4y + 4x) - –…

A: When a function is differentiated concerning a particular variable and the rest all the variables…

Q: 26) Find the partial derivative of of f= y cos x+ 2x sin z + 5y with respect to y.

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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: If f(x, y) = y² cos(x) – a° In(y), find the second partial derivative

A: Partial derivative problem

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

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Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

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

A:

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: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

A:

Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux  &  vx are the differential functions of x. To differentiate these type of…

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

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

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

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Q: Find the partial derivative. (2² + 4x – 4y)* z = dz

A:

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: Solve for the partial derivative with respect to x, y and z f(x, y, z) = x²y + xy² + 2xyz

A:

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

Q: Compute the partial derivative fxxyz for f(x, y, z) = cos(cos(x3 + z2 )) + x2 ln(y2 + z2 ).

A:

Q: Find the first order partial derivative with respect to y S(x, y) = a"y² + 3ze"

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Q: Find the partial derivative fx ( x , y ). f ( x , y ) = x ln ( 3x + 4y )

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

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: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: derivative

A:

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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

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Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

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

A: We will find an example

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

A:

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 both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x&amp; ∂z∂y

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

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 the first partial derivatives with respect to x, y, and z. 3xz W = x + y aw ax aw ay az

A: We will find the first partial derivatives as following.

Q: Let y=sqrtX. Find dy/dt when x=4 and dx/dt=3

A: →Use chain rule of differentiation.→dxndx = n xn-1     When n = 12         dx12dx = 12 x12-1…

Q: Find the partial derivative of u = x^2 + y^2 + z^2 - 4xyz

A:

Q: Find the first partial derivatives with respect to x, y, and z.…

A: The given function is f(x, y, z) = 3x2y − 5xyz + 10yz2

Q: Letv = x2sin(v) + vexy, where X = s + 2t and y = st-

A: Solution is below.

Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: Find the first partial derivatives of 3x – 2y f(x, y) = at the point (x, y) = (1,4). 3x + 2y af…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

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

A: Topic:- partial derivatives

Q: Solve for the partial derivative with respect to x, y and z f(x,y,z) = x²y + xy² + 2xyz

A: