Q2) Find az/du and äz/au for the following function and then find dz/ou and az/dv at the given points: z- 4e" In y, x In (u cos v), y=u sin v; (u, v) (2, 7/4)

Q: The y - cos X 3 2 =2y %3D

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Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

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Q: Find the derivative of y = In O O a.) dy dx =In(5) +4ln(x) —In(cosx) 4 1 dx X COSX b.) dy = c.) dy 1…

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Q: 2. Answer the following derivative related questions. dy. (1) Let y = x' + 4x³ + 2x² + 16, find ; dx…

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Q: 5. x² +7y° For the function f(x,y)= x° find f, fy, f,(-5,-4), and f (0.-2). + y

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Q: e-i.dt = lim X+ 00 V TE 0, Select one: a. b. NOT C. 8, O d. 1 O e. 0

A: According to our guidelines we can answer only first question. In first question we use the concept…

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A: For the directional derivative first find a unit vector in the direction of θ=π4 then take the the…

Q: 2. Find S'and S" for the function: S = + 2t2. Cos(t)

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Q: dy Find for the given implicit functions: dx а) у? - ху%3D2 b) 2.x sin (xy)– x = 0 c) (xe')" + y = 3

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Q: 04) Find dy /dx for the following functions: a) y².cotx= [sin(x.y)]-¹ b) y = (lnx + x)tan

A: See the answer below

Q: (3/5) What is the directional derivative Duf at the point (3, 1)? Let f (x, y) = x² - y and u =

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Q: Find df and dxo f , and write (dxo f )(X – Xo). (a) f(x, y) = x³ + 4xy² + 2xy sin x, Xo = (0, –2)…

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Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

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Q: IV. Implicit differentiation 1. xy + y? = 1, find y? 2. x²y – xy? + x² + y² = 0, find y' 3. x? – xy…

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Q: Show that the function y = x¹/², x > 0, is strictly concave

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Q: QIFind dx /1+x²/3

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Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

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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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