Suppose that f(x,y) is given, and that g is defined by g(s,t)=f(st,s^2−t^2) If ∇f(2,−3)=(−10,−8), find ∇g(1,2). ∇g(1,2)= What hypothesis must f satisfy?: f must be differentiable at

Q: find the directional derivative of f at p in the direction of B.  if f(x,y,z)=x+ycos(z) where p…

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Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

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A: Given query is to find direction derivative.

Q: (d) Let f(x, y) = 2x² + xy-y². Prove that the directional derivative of f(x, y) at point x = (3,-2)…

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A: Given that ψ=xz+y2and the direction vector2x⏞ -y⏞+3z⏞The point p0=(2,0,-1) To find the directional…

Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: Find the directional derivative of the function f(x,y,z) = tan (xýz) At point (1,2,3) İin the…

A: The solution is given as

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Q: 6. (a) Let f(x, y) = x³y*. Find the directional derivative of f in the direction of T = (3, 4) at…

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A: We know position vector of bee if it has a velocity vector  is We are given

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Q: Calculate Vf, V•f, V×f f (x,y. =)= xi+ y'j-* by the function

A: Introduction: The curl of the vector f(x,y,z)=fxi+fyj+fzk is given by ∇×f=∂∂xi+∂∂yj+∂∂zk×fxi+fyj+fzk…

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A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

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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: 4) Find the total derivative of the function: a.f(x, y) = ex²+y² 1 c. T(l,g) = 2₁ 2TT. b. z = x siny…

A: Total derivative of a function f(x,y) is given by df=fx dx+fy dywhere fx=∂f∂xfy=∂f∂y

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Q: 2) r(1) = ti –t j-tk, t20 Draw the graph of the vector-valued function, explaining it in detail.

A: The general form of the parametric equation of the curve in three dimensional space is given by ,…

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Q: Let f(x,y) = (x² + (G))°. Determine the directional derivative of f at the point (1,0) in the…

A: Explanation of the answer is as follows

Q: Find the directional derivative of ø = x² + y² + z² at point (1, 2, 1) for a direction determined by…

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