Given f(x,y)=3.xy² -2y+5x²y° . (i) Compute the first order derivatives f, (x, y) and f,(x,y)· (ii) Compute the second order derivatives f,., (x,y), f(x,y) and f,, (x, y) (iii) Determine the value of f(-1,2)·

Q: 4- find the second order partial derivative w.r.t each variable g(x, y) = x*y+cos(y)+ ysin(x)

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Q: Given f(x, y) = x²y – 2xy + x² – 2x + y² – y. (a) Find the critical points of f. (b) Use the Second…

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A: Directional derivative using gradient

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

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A: To Find: Directional derivative

Q: Q1: Find partial derivatives of the function with respect with each variable 1) f(x, y)=2x² − 3y – 4…

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Q: 6.) Find the directional derivative of g(x,y)=Vx² +y² at the point P(3,4) in the direction of v…

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A: We have given function, we have to find directional derivative.

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

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Q: Could I get help finding all the second order derivatives please?

A: Given

Q: 1 Find the direction derivative of f(x, y, z) = x²y -zx -y³x at the point (1,-1,1) in the direction…

A: Directional derivative

Q: 2. Given the function f(x, y)=3x²y + 2xy-y, a) find the value of the directional derivative of the…

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Q: Find the derivative of the function at P, in the direction of A f(x, y) = 2xy-3y, P(5,5), A = 4i+ 3j…

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Q: 3 + y? 1² + y si æ + -y? f(x, y) , si a = -y?

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Q: Find the derivative of the function f (x, y, z) = -9x + 5y – 10z at the point (-3, 6, 5) in the…

A: we have to find the following . I have explained in details please see the explanation and if any…

Q: 1. Find the directional derivative of the function f(r, y, 2) = 3e" sin(ry) in the direction of v =…

A: 1.directional derivative formula = depf.n Del f = i∂f/∂x + j∂f/∂y+ k∂f/∂a given f = 3exsinxy…

Q: The directional derivative of f(1, y) at the point P = (0, 4) in the direction of the origin is -2.…

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Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in the…

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Q: Find the maximal directional derivative magnitude and direction for the function…

A: Consider the given function and point, f(x,y)=x3+2xy-cos(πy),(3,0) Now, find the derivative with…

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A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

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Q: The directional derivative of f(x, y) (3, 4) is -In(x² + y²) at the point P(1, 5) in the direction v…

A: Definition used -          Directional derivative at the point -     The rate of change of f(x, y)…

Q: Find the Partial Derivatives of the functions with respect to each variable 4) f(x,y)=\x² + y?

A: We have  f(x,y)=x2+y2 So we can write f(x,y)=(x2+y2)12 And we know that ∂(xn)∂x=nxn-1

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Q: 6. Given f(x,y)= %3D y a) find the directional derivative of f(x,y) at (1, -2) in the direction of…

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Q: B. Use the definition of directional derivative to solve Duf(x0, Yo, zo) at point P(xo, Yo%o) where…

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Q: 3. Find the derivative of the function f(r, y, ) = xy + yz+ the direction A = 3i + 6j – 2k. zr at…

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Q: 0Y Find the direction derivative of fcxy)=xy at the paint (2,1), by the dirction of v- i-j

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Q: 6- find the second order partial derivative's of the function : z = x sin sin (x²y)

A: Here i am providing my handwritten solution

Q: Consider a function of 3 variables h (x, y, z2) = -3 (2+ Calculate the value of its third order…

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Q: a) If W = F(x ,y),where x =v²-g and y 2vg calculate W +W, %3D b) What is the directional derivative…

A: W=f(x,y) and x= v2-g2 & y=2vg   Wx = dW/dx = (df/dx*dx/dv) + (df/dx*dx/dg) ..............From…

Q: 3x The directional derivative of f(x,y,z) = ln (주)을 1+yz from P to Q(-1,-1,2) is given by...…

A: We can solve this using given information

Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: a) By using partial derivatives, calculate the slope of the tangent plane for the following…

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Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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Q: (2.2) The directional derivative of f (E, y) at P(1,2) in the direction of i+j is 2v2 and in the…

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Q: 2. Use suitable linearization to find the approximate value for the function at point P. f(x,y) (x-…

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Q: 2 - What is the directional derivative of the function f(x, y, z) = x° - 2xy + z point A, = (1,1,0)…

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Q: 3 Find the directional derivatives of p = 8xyz³ - 2x²y²z² at the point (2,-1,1) in the direction 21…

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Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: 23. Find the directional derivative of f(x, y) = *+y at P(1,0) in the direction of Q(-1,-1).

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Q: Find the derivative of f at point P in the direction of u. f(x, Y, 2) = 9a² + 2y² – 72², P = (6,7,…

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Q: Find the directional derivative of f(r, y, z) = e cos(ryz) at (0,1,) in 2 - 1 I- 2 the directions…

A: We have to find the directional derivative of f(x,y,z) at 0,1,12 in the directions parallel to the…

Q: Let f(x, y) = -4x + 3y. Find the directional derivative in the direction of v = from the point P =…

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Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: 1. Find the directional derivative of the function f(x, y, z) = 3e" sin(ry) in the direction of v =…

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