Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) = e">t, r1, r2 ER (b) yı(t) = cos(at); y2(t) = sin(at), a e R (c) y1(t) = cosh(at); y2(t) = sinh(at), a E R

Q: Find the directional derivative of the function xy2 + yz2 + zx² along the tangent to the curve x =…

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Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

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A: Given fx,y=lnx3y6     at (4, 3) The linear approximation in 2 variables is given by Lx, y=fa,…

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Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz ,at the point P. (0,0,0) in the…

A: We have a given function g=3e^x cos(yz)

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Q: Ift=2cos (y² + 2), find the derivative of t with respect to y. A. 8y sin(y² + 2) cos(y² + 2) B. –8y…

A: The given function,  t=2cos2y2+2

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Q: 12. Find derivative of the following composite function using the Chain Rule: 2y t(y) = 6y² + 1+y?…

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A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

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Q: (a) Find the derivative of ƒ(x, y, z) = x3 - xy2 - z at P0(1, 1, 0) in the direction of v = 2i - 3j…

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Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

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Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

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A: Given

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A: We are asked to find the derivatives.

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A: We can solve this as follows:

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Q: 2. find the derivative of the function g(x, y, z) = 3e* cos yz,at the point in the direction of A =…

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A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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Q: 21: dz 22: Find the derivative of f(y,x) = xe?y + cos(3yx) at a point (1,0,7)in the direction of V =…

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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 gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve