Find a2z given that z is a differentiable function of x and y, and xz + yz3 = 2 + x²e♥

Q: b) Let f be a differentiable function of one variable, and let z = f(3x² – 5y²). Show that az əz…

A: Given  z = 3x2 - 5y2

Q: Suppose that y and z are twice-differentiable functions of r. Show the d y dr y z %3D y"

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Q: determine whether the piecewise-defined function is differentiable at x = 0.

A: We first find the Right and left-hand limit of f'(x)

Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: Assume that f(x, y) is a function given by f(r, y) = r + y? +x²y+ 4 on a domain D = {(r, y) | |r| <…

A: Given:

Q: yyx² +y? F(x,y) = - is a homogeneous function of degree

A:

Q: Do not simply the answer. Determine ∂2z/∂x2 given that z is a differentiable function of x and y,…

A: Given xz + yz3 = 2 +x2ey

Q: Locate and classify the local extremum of the function f (x, y) x² + y? – 8x – 2y + 6. | -

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Q: Let f (2) be an analytic function, which is represented by f (2) = u (x, y) + iv (x, y) where z = x…

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Q: Prove that y = x- 2 is differentiable and calculate y'.

A: Given: The function, y = x-2

Q: Find the domain of the function f(x,y)= exy/ x-y2

A: Answer-

Q: Find the absolute maximum for the function f(x,y) = 7 +6x2 +6y2 bounded between x = 4, x = 7, y = 5…

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Q: Determine the interval (s) on which the function f(x) = 3xe* is concave down. O 号

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Q: 3. Find expressions for frz and fyy for the multivariable function f(r, y) = x²y+ yr %3D

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Q: Find the interval(s) where the function y = x – 2x² – 7x + 2 is concave down. Justify your answer.

A: Find the double derivative of y and then equate it to zero.

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: For the function f(x.y.z)= 3+5xy"-2z*, find f,, f, and f. -口 fx = 5-口 fy=

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Q: Find ∂z/∂x for1/x+1/y+1/z= 1. Assume that the equation implicitly defines z as a differentiable…

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Q: faow that the function f depthed by (X .Y) = (1, - 1) f(XrY) = %3D x2 + 냉 (x, y) $ (1,-1) * ty is…

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

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Q: Find the domain of the following multivariable functions b. f(x,y,z) = x/y+ In (z – 1) c. f(x,y,z) =…

A: Solution:Domain: The domain of a function is the set into whcih all of the input of the function is…

Q: c = sec t, and y =

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Q: dy 6. If y is a differentiable function of x and r + 2y3 x² = 8y?, then find dr

A: This question is based on diffrentiation chain rule.

Q: Find fyry. f (x, y) - = x"y" – 9x°y + x f yry %3D

A: Partial derivatives are calculated with respect to y then x and again with respect to y.

Q: Suppose that y is a differentiable function of the variable x. Find y' D↓x y of 5x³y-7xy² = 3 +7y

A: Given that:5x3y-7xy2=3+7yTo find Dxy or y'

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

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Q: a2z Find given that z is a differentiable function of x and y, and xz + yz3 = 2 + x?ev

A:

Q: Let

A: We will find the partial derivative with respect to x.

Q: Find fyay. f(x, y) = x"y" – 9r'y + x x'y' 9x°y + x f yzy %3D

A: Solve by differentiation

Q: Select the function whose domain is the region below. 4 8. f(x, y) = v /16 – x2 – y² + /8x 2² – y? |…

A: Ans is given below

Q: Determine whether z is a function of x and y. z + x ln y − 8yz = 0

A:

Q: Let y be a differentiable function of æ. Find , if x3 – 2y2 + xy = 0 at (1, 1) [Hints: using dy dr…

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Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: Determine the set of points at which the function f is continuous. x² + y? f(x, y) ={ Jx² + y² +9- 3…

A: In this,we check the continuity of given function f(x,y) at (0,0).

Q: For which values of a ER is the function f(r + iy) = (a²x – axy) + i ax? + ay %3D an entire…

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Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

Q: В. Find az if z = f(x, y) is implicitly defined as a function of x and y for the equation below…

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Q: Suppose y is a differentiable function of r. Find y' if 2xy 3 2y3 + 5x4. y2 -

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Q: Suppose that y = f(x) is a differentiable function for which the following information is known:…

A: Suppose we have given function y=f(x) is a differentiable function and some information about…

Q: The set of all points where the function f(x) = i-e¨ is differentiable is (A) (0 , ∞) (B) ( –0, ∞)…

A: We find the set of all points where the given function f(x) is differentiable.

Q: Find the domain of the following multivariable functions (answer two) f(x,y) = /4 – x² – y b.…

A: (a) Given that           f(x,y) = 4-x2-y2   Domain:       Since                      4-x2-y2⩾0 ⇒…

Q: If f : R → R is a differentiable function, then f has an antiderivative over [0, 10]   TRUE OR…

A: Answer is below

Q: Let f be an arbitrary differentiable function of x, y and z, and let x = 2u-v. y =v-2w and z = w-2u.…

A: Given: f is arbitrary differentiable function of x, y, z and x=2u-v, y=v-2w and z=w-2u. To find: The…

Q: Find the absolute maximum and minimum of f(x, y) = 1x + 5y within the domain 2² + y? < 1². %3D

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Q: Show that the function d: RxR → R defined by d(x, y) = √x-y

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Q: Define for a function rasls, y. 2) - slelo), 0), alo) where and, are differentiable functions.

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Q: Suppose f is a differentiable function of x and y, and g(r, s) - f(5r – s, s² - 6r). Use the table…

A: We use chain rule to find out partial derivatives

Q: Let fbe a differentiable function such that f(1) = nand f(x) = Vx3 + 6. What is the value of f(5)?

A: ∫xn=xn+1n+1