18.) Compute the directional derivative of f in the given ✓ given points P. 3 a) f(x, y, z) = xy² + y ² z ²³ + Z²x₁₂ P = (4-2₂³¹1), V = 1 Ju (i +3j + 2k) (1 12 3 b.] f(x, y, z) = xyz, P = (e₁e₁0), V= 13₂ | +istisk 13 to

Q: f(x, y) = ln(-6x – 4y), (5,6), A=6i + 8j 14 17 A) 135 135 B) C)/17 D) 11 135

A: Duf=∇f·uu

Q: 2. Find the directional derivative of f(x,y) = x cos y in the direction of v = 22, -1). A. (2 cos y…

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Q: 1. Find the derivative of the following: 1² + 2r + 1 a) f(1) = r3 - 5x + 3 b) G(2) - VP+1 dt e) y…

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Q: 1. Which of the following functions have a derivative of zero? a) y = 9.8 b) y= 11 c) y=-4+x d) y =…

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Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

A: The given function is fz=cscz=1sinz. A function fz=ux,y+ivx,y, satisfies Cauchy Riemann equations…

Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: 15. Differentiate 4y³ with respect to x. A) 12y? B) 12y C) 12y2 dy D) 4y2 dy dx dx 16-17. Find the…

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Q: Find the gradient Vf and the directional derivative at the point P (1,–1,2) in the direction a =…

A: The given function f(x, y, z) = x3z - yx2 + z2.The gradient of a function f is defined as∇f(x, y, z)…

Q: Find the relation of the derivative of y and y with respect to x, given that yx-y? = 3x 3x II. 1-2xy…

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Q: g(t) = V(1 – 3t)4 + t4

A: