4. Suppose that y = y(x) is a differentiable function which is defined near x = 2, satisfies y(2) = -1 and x' + 3xy +y =9. Use the linear approximation to the change in y to approximate the value of y(1.91).

Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Find the first partial derivatives of the given functions with respect to each independent variable.…

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Q: Find the requested partial derivative. dz 3 if z° = z+ xy - 1 and y = x+ y- 1 dy 3

A: We have to find partial derivative

Q: Determine the second-order partial derivative for the indicated function f(c,y) = cos(2x² – 3y?)…

A: Partial derivative of a function g(x,y) with respect to x is the derivative of g(x,y) keeping y…

Q: Find ðw/as and dw/at using the appropriate Chain Rule. Function Values w = y³ – 10x3y x = e°, y = e…

A: Given  w = y3 - 10x2y x = es   y = et

Q: Find for the following equation by Implicit Partial Differentiation; дz x³ + y²z4 + 3xyz = 5

A: Implicit partial differentiation

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

A: Partial derivative problem

Q: Find the differential of the function y=√x3+4x at x=2.

A: Given the function:

Q: Find the value of dz at the point (1)1, If the equation 5xy+ z4x -Qy2 =4 %3| defines z as a function…

A: Given 5xy+z4x-2yz=4to determine dzdx  at  (1, 1, 1)

Q: 3. Find the partial derivatives du and ou if uw = x sin (y), x = s² +t? and y =;,

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Q: z = x3 – xy? + 3y² |

A:

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

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Q: Find the partial derivative dz for the function z = cos(x³ +y²).

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

A: We will find out the required value.

Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

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

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Q: 2. IShow, using the definition of the derivative, that the function f(x, y) differentiable at every…

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Q: Find the indicated partial derivatives. y+ Sz az dy ex

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Q: Find the Partial derivative of f with respect to y for * 2. y² f (x, y) = x + y

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Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: Find the partial derivative Əz Əx for the function z = 8y²√x.

A:

Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: Find the solution of the differential formula in partial derivatives = x³ sent +1; y(x,t);…

A: Integrate twice with respect to t and then put conditions

Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: Solve for the second (a) own partial and (b) cross partial derivative of the function below x² + y²…

A: On solving this we will get

Q: Let h(x) = e*. f(x) and assume that f(ln 4) = -5 and f'(ln 4) = 6. Find the equation of the line…

A: We have to find equation of the line tangent to y=hx when x=ln(4)

Q: If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

A:

Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = sin(2x + 3y) x = s+t,…

A: We can answer both the answer as below.

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

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: If z=(x+y)e^y and x=7t and y=1−t^2, find the following derivative using the chain rule. Enter your…

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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: 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 the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

A:

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

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Q: If z = (x + y) e and x = 3t and y = 1 – t, find the following derivative using the chain rule. Enter…

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

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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: (e) Use a backward finite difference approximation to approximate the first derivative of the…

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Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

A:

Q: 10. Use the Chain Rule to find the indicated partial derivative if ax F = Vu? + v2 + w², u = xe, v =…

A: F=u2+v2+w2To find ∂F∂x

Q: Find the mixed partial derivative at the point (2, 3) for h(x.y) = x sin(y) + y sin(x) + xy

A: The given function is, Differentiate the above expression with respect x partially.

Q: 1. if z = a² sin[e!n 2y] + 3xy cos[e!n2x] – 4a?y², find the partial derivative of z with respect to…

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Q: Find aw/as and dw/at using the appropriate Chain Rule. Function Values w = sin(8x + 9y) x =s+t, y…

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Q: find the partial derivative of the function with respectto each variable. h(x, y, z) = sin (2πx + y…

A: We have to find the partial derivative of the function with respect to each variable   The given…

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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

A: