52. If z = f (x, y), where x = r cos 0 and y = r sin 0, find a. Əz/Ər, b. дz/80, and c. d z/Ər d0.

Q: 37. ; with r = 1 andh = ;: 0, p2 sin¬! V1-h² /r²-h/r2-n? (0,, 33 47-3/3 (0, 0.71)

A: Let's simplify in steps Let's take the numerator first:

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A: If z = cos (x + ay) + sin (x - ay), with a ∈ R, then the result of a(∂z/∂x) + (∂z/∂y) corresponds…

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Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

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Q: -s Jatx? 3. 4-/ sinx coss dx |

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Q: Gren thint sin (A+i6) = xtiy, 28 Prove that, 9父+ =1 snh'B 1) x essec?A -y' sec'A =1

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Q: 4. Evaluate: S. yx²dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t?, (0 <t< 1).

A: A line integral is the integral of a function along a curve. The function can be scalar-valued or…

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Q: @ / Find if dy O J= \ntanh (+2 の= Cos (Cosスー) O3=109,(e CSCX +Sinx)

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Q: * Q9 If y = cos(x + y)dx + (3y² + 2y + cos(x + y)) dy = 0, then M = cos(x + y), N = 3y² + 2y Ttue…

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Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

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A: differentiate with respect to x

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Q: If f(x, y) = x cos y + yex, find d2f/dydx.     −sin y + ex     −sin x + ey     sin y + ex…

A: Note the differentiation results : d(ex)dx=exd(xn)dx=nxn-1d(cosy)dy=-siny

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Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: 6. If x= sect and y=tant, evaluate at t =- of the following: dy (a) dx d'y (b) dx?

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Q: 1. Differentiate F(t)= e4t° sin sin 2t [Hint: y = e", u = 4t³ sin 2t.]

A: In this question we have to solve the differentiation of the function.

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A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

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Q: 2²y ds, C:x = cos t, y = sin t, z = t, 0 < t < a/2

A: