Evaluate [3r* sin(ryz) + r*yz cos(ryz)]dr + r*z cos(ryz)dy + r*y cos(ryz)dz where C is given by F (t) = te'i +t cos(t)j + (1+ t)k, 0 st<1.

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A: The given function is

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A: Given: f=sinxycosyzcotxz To find: fzyx

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Q: Q3) Simplify (if necessary) then Compute: y"+ 2y Where y(x) = (zx+ cosx*)] [4(cosh2x-sinh2x)] d 2,2…

A: To find -  Simplify (if necessary) then Compute : y'' + 2y' where yx = ∂2∂x ∂zz2x + cosx44cosh2x -…

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Q: 10. sec (10t) tan" (10t) dt 11. tan" (2w) sec" (2w) dw / cot (3r) csc® (32) dæ 12.

A: As per our guidelines, I can answer maximum one question. Since you have asked for three, So i did…

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A:

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A: I have used the rule for composition of function and multiplication of functions

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A: we have to find Laplace transform

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A: According to question given thatf(x,y)=3x3 cosy-y2 sinx-2x ln(y)-y ln(x)-4x2y

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Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

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Q: Find div F and curl F if F(x, y, z) = 9ei - 3 cos y j + 2 sin² z k. div F= curl F=

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Q: How did he get the value inside the circle f(x, y)=x² + sin(xy) Vf=x*+sin(xy)) i+ d(x²+sin(xy)), dx…

A: given ∇f(1,0)=2i+j we have to find the direction in which the directional derivative has some value.

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A:

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

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A: We have to prove

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Q: a3 f 2- Find the third derivative for for f (x, y) = sin əx3 -2sin?cos()+2 sin) sin By'sini )+2…

A: The given function isf(x, y)=sinxy

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Q: Now H= [² 2 id 2² H эрг = Ho 2² [Ho Sin (Kr_wt)] ar 2 [2 Ho Sin (Kr- wt) Ho 2/ [cos (kr-wt) x] K Ho…

A: They have derived the partial derivative. Our aim is to explain the derivative rule.

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A: Solve for the equation for the derivative

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A:

Q: Let f(x) = 8 sin r + 3 cos r f'(x)- f(똥) =|

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A: This is a application of integration problem

Q: Find the derivative (dy/dx) of the following functions: I) y = (sin x + cos x) sec x

A: Since there are multiple questions present, according to company policy we will be answering only…