f(x, y) = e sin x, P(0,0), Q(2,1)

Q: Let f = zy + yx, v = [y, z, 4z - x], w Find - [vª, zª, x®]. (a) grad f and f grad f at (3, 4, 0) (b)…

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Q: determine directional derivative f(x, y) = x²y³ – 4y on point (-1,2) on vector direction v = (2, 1).…

A: The partial derivatives of f at (x,y)=(-1,2) are : ∂f∂x=2xy3   and   ∂f∂y=3y2x2-4. Therefore,…

Q: - g(4)= <F 1 • g(x)= x² +. 5

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Q: Find both partial derivatives дz ?х дz and for the equation exy + yz² = x³yz ду

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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 dx (1+x²)3/2

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Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

Q: Let h(x, y, z) = ln(x² + y² + z²). (a) What is the direction of maximal increase of h at the…

A: Given function:  hx,y,z=lnx2+y2+z2 To find: a) Direction of maximum of h at the 1,1,1. b) The…

Q: P= (3,2,;?)

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Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

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Q: How can you use directional derivatives to estimate change?

A: Let f be a differentiable function. The directional derivative of f in a particular direction at a…

Q: cos (5x-0.1) w(x) =- e*

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Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: f (x, y, z) = arctan(x² + 2y + z) At the point A(0,1,0) along the direction ñ, where n is the…

A: Given that f(x,y,z)=arctan(x2+2y+z)  For a function of three variables f(x,y,z), the directional…

Q: III. Encuentre la derivada direccional de la función en P en dirección de Q 11. f(x,y) = x² + 4y²,…

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Q: 1 t3 4u p 1.A (p, t, u) pt2 u? 2. g(x, y, z) = V² +z=2 + sin(ry – x²)

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Q: Find

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