Let F(x, y) = x² + y°, ¤(t,s) = s cos t, cost, y(t, s) = s sin t Then OF 3 -2s? cost sin t+ 3s° (sin t)² cos t -2s cos t sin t+ 3(s sin t)² cos t 2s cos? t + 3s² sin' t none of the listed here

Q: a3 2- Find the third derivative for = sin(÷) for f(x, y) ax3 -2sin?cos()+2 sin A:- ) sin()+3cos )…

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Q: dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

A: Solution: As per our guideline we are supposed to answer only first three question please repost…

Q: F(x) = 1+e siny x %3D -- = -15 e sin4X- se"co54X fca) = fco) = -8 R fくり) = fci-2) = 4.2398 > KMS %3D…

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Q: What is the equation of the curve whose slope at any point is equal to y cot x + tan?x and which…

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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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: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and 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.

Q: Show that a fuinction F:R>R defired by 3 If I=y=0 1S continous ert (o0)

A: Continuity: Let a function f(x,y) be defined on an open disk B containing the point (x0, y0). A…

Q: 30. (cosa tan x) = O A OB O OD (A) secr+sina tanz (B) (C) (D) cos x - sin rsec²r sin r

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Q: 2y y+cos x 2 + 2y + cosx Find f, if f(x, y) = (y)² COSX A O 2sinx (y)²secx + 2y + cosx C 1 (y)² + y…

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Q: V. Find the third derivative: 1) y = 10 tan(x) - 2 cot(x) 2) y = x³ - x² sin (x) 1 3) y = 2 sin(x)-4…

A: The given problem is to find the 3rd derivative of the given functions.

Q: (y? cos x – 3x?y – 2x) dx + (2y sin x- x'+ In y) dy = o

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Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: Find the derivative of i) y = 3* ii) y = cosec 2x 1 iii) y = sin ¹4x

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Q: Question: Find the derivative. y = 2/T sin /T Select one: sin /I y' = cos /T + cos/r y' = sin /I +…

A: Topic:- derivatives

Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…

Q: The derivative of y = 4cosxsinx is: ○ a) yl= 4(1 — 2 sin² x) b) y/= -4 sin x cos x c) dy = 4 sin x…

A: To determine the derivative of the following function.

Q: 2. (5) Find f, for the function f(x, y) = sin (x + y²)

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Q: 1- find dy/dx as a function of x. y = sec (tan x)

A: As per bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: EX/ find (dy) for function y= banx + — — ban²³x bản dx H-W EX/ find dy for function y = T+ Cost Sinx…

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Q: Find fy for f(x, y) = (In x) (sin x² y). O fy = (In x)(cos x²y)(2xy) O fy = (cos x2y)(x²) O fy = (In…

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