Let f(x, y) be a C-class function of two variables (i.e. its first order partial derivatives are continuous). For a composite function of one variable h (u) = f (-u® +3 u, 3 x® +4 u) = f (-u° + 3 u, 3 uº + 4: find the value of derivative h'(u) at u = 1 given fæ(2,7) = 0 , fy(2,7) = 2 .

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 2x²y - 4xyz + 6yz²…

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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: If z = f(x, y) has continuous second-order partial derivatives and x =r* +s² and y = 2rs , find a)…

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Q: If u = f(s, t) has continuous second-order partial derivatives and s(x, y) = 8x² – 4y*0 and t(x, y)…

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Q: Find the first partial derivatives of the function. f(x, y, z) = x²yz° + 7xy – 4z fx(X, y, z) =…

A: Partial derivative is like normal derivative but at a time differentiate with respect to one…

Q: Find the second order partial derivatives and of дхду aydx S(x.y) = 4x + In x + e² cos y + 9y + 3

A: d/dx(x^n)=nx^n-1 d/dx(cosx)=-sinx

Q: Find the first partial derivatives of (a) f(x,y,z)=x²yz³ (c) S(x,y,z)= In(#)+ tan""(yz) (b)…

A: Solution of first partial derivatives.

Q: Find the first partial derivatives of the function. 4x – 7y f(x, y) = %3D 4x + 7y A(x, y) = Wx, y) =

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Q: Find the first partial derivatives of the function. F(x, y, z) = xz – 9x^y^z° %3D fx(x, y, z) = %3D…

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Q: (d) f (x,y) = ln (4x – 5y)

A: The given function is fx,y=ln 4x-5y. The second order partial derivatives are fxx, fyy and fxy.…

Q: Compute the partial derivative of the function * f(x, y, z)= el-roos(y) +2e=1/(1+²)

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Q: If z = f (x, y) is a function that admits continuous second partial derivatives such that: V f (x,…

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Q: Find the first partial derivatives with respect to x, y, and z. 7xz x+y

A: This question is related to differentiation, We will solve it using given information.

Q: Find all the second-order partial derivatives of the function. r(x.y) = In (x + 3y) дудх дхду dy II

A: Given function is rx,y=lnx+3y Differentiate partially rx,y=lnx+3y with respect to x…

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x²y – 9xyz + 8yz2…

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Q: If f (x, y) is a homogeneous function of degree n in x and y and has continuous first and second…

A: This question is based on Euler's theorem statement.

Q: Find the second order partial derivatives of the function: f(x,y)=x* +xy° +x+4.

A: In the case of function of two variables there will be a total of four possible second order…

Q: Compute the given partial derivative. f(x, y) = 8 sin(4x² – y), (0, 1) f,(0, 1) = %3D

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Q: .    Given y = (x, z) = 6x2 + 3xz4 where X(B, E, T) = B2 + 2E + TB Z(B, E, T) = (ETB)1 + B + E…

A: Given that,  y = (x, z) = 6x2 + 3xz4 where X(B, E, T) = B2 + 2E + TB Z(B, E, T) = (ETB)1 + B + E…

Q: S (x, y) sen (r2 – 0²) + In(r0 + 0), con Væ2 + y? A r = arctan

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Q: Find the first partial derivatives with respect to x, y, and z f(x,y,z)=4x^2y-5xyz+7yz^2 fx(x,yz)=…

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Q: Given that z = 2(r, y) and ze™" – a³z + In(x°z³) = 0, find the value of the partial derivative z, at…

A: We have to find the partial derivative zx at the point 1,0,1 where zexy-x3z+lnx2z3=0.

Q: Find the first partial derivatives of the following function. F(w,x,y,z) = 4w 4x + 9y + 5z Fw = Fx:…

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Q: a) f(x, y) = (4x²y4 – 3x² + 8y³)³ x + y c) g(x, y) = In sen b) f(x,y) = x ln y + y ln x

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 8xyz + 7yz?…

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Q: What does the Clairault Theorem claims?       For any function F(x,y) its partial derivative with…

A: It is asked to define Clairaut's Theorem

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 6xyz + 10yz %3D…

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Q: Evaluate the first partial derivatives of the function at the given point. f(x, y) = 9e* In(y); (0,…

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Q: Find all the second-order partial derivatives of the function. r(x.y) = In (2x + 3y) дудх дхду dy?

A: Given that r(x,y) = ln(2x+3y) We need to calculate all the second order partial derivatives. The…

Q: (b) Show that the function f: R2 → R given by (* if (x, y) + 0, S(x, y) = 0 if (x, y) = (0, 0), is…

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Q: Find the second order Partial Derivatives of the functions with respect to each variable 3) r(x, y)…

A: Second order partial derivative will be  ∂2r∂x2 , ∂2r∂y2 , ∂2r∂x∂y , ∂2r∂y∂x

Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 3x2y – 6xyz + 10yz?…

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Q: Find the first partial derivatives of the function. ах + by cx + dy f(x, у) fx(x, y) = fy(x, y)

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Q: Find the first partial derivatives with respect to x, y, and z. f(x, y, z) = 4x²y – 7xyz + 6yz?…

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Q: 1)Consider the function f(x, y) = x° + 2xy + y? – 5x b) Calculate the second-order partial…

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Q: 다음 함수 /의 2계 편도함수를 모두 구하여라 (1) fx, y, 2) sin (xy) cos (vz)

A: As per Our guidelines we can solve maximum one question u can repost other's in next question

Q: Find all the first order partial derivatives for the following function. f(x, y, 2) %3 2(e Х) У af…

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Q: 2. Suppose that f (x,y) is a function so that f(x, 1) = e*- 3x + 2 f(0,y) = y2 +2y Find the partial…

A: We use the definition of partial derivatives to find the partial derivatives.

Q: Find the partial derivative for the function f(x,y)=√x+y3 f(xx,y)= f(x,y) = √8x + y² 33x √8x+y³ (y)=…

A: The given function is;  f(x,y)=sqrt(8x+y3).

Q: Solve for the indicated higher-order partial derivatives, fæx, fæy, fyy- · f(x, y) = Vx² + y?

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Q: Show that the function ху si x? + y? + 0 f(x,y) = {x² +y² si (x.y) = (0,0) It has partial…

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Q: -2x+3y h(x, y) = p(t) dt . ry

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Q: Let f be a function with continuous partial derivatives and defined by: z=x2*f3(xy,y2) If taken u…

A: We will find out the required value.

Q: Find the second order partial derivatives дхду of and дудх f(x,y)= 4x² + In x + e*** – cosy +9y +3.

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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: Show that the mixed partial derivatives fxyy, fyxy, and fyyx are equal.                 f(x, y, z) =…

A: Given : f(x,y,z)=e-xsin(yz)To find: fxyy=?,  fyxy=?,…

Q: Find the first partial derivatives of the function. f(x, у) : cos(t5) dt fx(x, y) = fy(x, y) =

A: We use the leibniz derivative.