d?y taby = Fo cos ot, where wo, ware positive con- dt- stants, and Fo is an arbitrary constant. You will need to consider the cases w + wo and w = an separately.

Q: dw If w = x'y sinz - 3zexy, find dz O a. dw =x?y cosz - exy dz %3D O b. dw =2x2y cosz -exy dz Oc. dw…

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Q: If u = x² cosy+ ye", where x = s+2t and y = st, prove that ди ди 2- (s – 21) (x siny- xye – e"). -…

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Q: dz dt Consider x = cos t, y = sint and z = x2 +y². Then ulan ||

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Q: If f(#) = | cos(t) dt, then f'(2) = s(t²) dt, then f'(x)%3= COS Select one: a. 3e cos(2) CoS b. e…

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Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: Find dy/dt and d^2y/dt^2 for function aln(y)+b cos^2(ty)=2t^3 where a  and b are certain constants.

A: Derivative two times simultaneously and use the forma for derivative

Q: in term of t, if w -+, x= cos t,y sint and z in term of t. if w = xy, x = cost and y = sint, whent=.…

A: 4. Given data is : w=xz+yz , x=cos2t , y=sin2t  and z=1t To express dwdt in terms of t

Q: Solve the diferential egyatien dy - by Melne's méthool with h-o-1 e Cosx dx

A: GIVEN: y'=e-xcosx-y   The formula is: yn+1,p=yn-3+4h32yn-2'-yn-1'+2yn'    ............(1) Put n=3,…

Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: suppose that w = x² + y2 + z2 x = cos) y = sin) z = tanOUse the chain rule to find dw V dA ! dw dy ,…

A: topic - derivatives

Q: Let 7 (t) = < - 2 cos(2t), Find F(t)dt (don't include the +C)

A: Please refer to the image below.

Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: Transform the equation dy = ry into a variable da separable form. O vydy = xdx dy dy Vydy de %3D

A: We will transform the given equation into variable separable form as shown below

Q: u" (x) = -u(x), 0 < x < T, и(0) — и(т) — 0.

A: Step:-1 Given differential equation of second order is  u''(x)=-u(x), ----(1), with u0=uπ=0 and…

Q: Q3: Show that b. I — = ƒ‰e¯¹8(2t − 2). dt = ½-½ 2e C. L²u(t)dt = = [cosnt. 8(t − 2) + 38(t+1) +…

A: We have to prove the given statement.     According to our guidelines we can solve only three…

Q: π/3 So, f²ef/³ t In u tans ds du dt

A: Given problem:-

Q: 51. Let s= cos 0. Evaluate ds/dt when 0 = 37/2 and doldt = 5.

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Q: If r(t) = (2 – 3t2)i – 5tj + 3 cos tk, what is it's acceleration? Select one: O a(t) = -8i +3 sin tk…

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Q: 18 Compute r''(t) when r(t) = (t°,9t, cos t). r'(t) = OID

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Q: Suppose w = x = cos? t, y = sin? t, z = dw Evaluate at t = 3 , by using the Chain Rule dt

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Q: If æ? + y? = 25 and dy/dt = 6, find %3D dæ /dt =

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Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

Q: Verify that the indicătéd function is an exp for each solution. y" - 6y' + 25y = 0; y = e3x cos 4x…

A: Recall: (uv)'=u'v+uv' where u and v are the function of x

Q: If f(z) = cos(t) dt, then f'(z): COS %3D Select one: a. 3e cos(z) COS b. ez cos(ez) c. 3e cos(e)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: d [sin(t) dt = sin(Vk), Where k is cons tant Select one: O True O False

A: Anything inside the root should be greater than 0.

Q: Let z = x?y + 3xy+ where x = sin 2t and y dz find = cos t. Use the chain rule to when t = 0. dt

A: See solution below. Using definition of chain rule.

Q: Is f(x, y) = sin?(xy²) a solution to the PDE sin(xy²) > 0? Je * Je ax ;= (2x + y)(2y) cos(xy²)/F…

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Q: - (7- dy sin2x ) dx = 0 y y

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Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: If and x = 2t, y = 5t, then the value of equal to 12. z = x - 2y, Select one: O True O False dz dt…

A: Given that , z=x-2y and x=2t , y=5t find dzdt at t=3.

Q: Q9. If W = f(u)=u³ +sin ¹u+lnu, and u= ax +by, where a, and b are constants, show that aw Əw b oy Əx

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: If u = x3 + y3 where x = a cos t, y = b sin t, then du dt

A: Solution

Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Assume that y= 5x and de/dt = 2. Find dy/dt. Select one: 10 O 5 O 2 1

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Q: Consider r (t) = ( – 4t² + 3, 2e“, 4 sin(5t)). Find F(t)dt. Don't include the +C. frwa = %3D

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Q: Solve the fello wing differntial equation by ieg Lapla ce trans frmation dy +2y=0, dt , where…

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Q: Given f(x,y) = ex cos y, Evaluate fx(0,2) O e² 00 O cos 2 O-sin 2 M

A: We have to find the derivative

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: f : [o,s] → A? flt) = ( 6E) 2 cosh 3t, - 2 sin 3t, Compute f'lt).

A: If f(t) is differentiated with respect to t, then f'(t) is obtained. Let f(t)=x(t), y(t), z(t), then…

Q: If r = sin (ƒ(t)), ƒ(0) = pai/3, and ƒ′(0) = 4, then what is dr/dt at t = 0

A: Given: