dy If tan(ry) + 5 = ry then show that dr? 2y

Q: If sin y =x sin (a +y) then show that dy sin (a +y) (a is not multiple c dx sin a

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Q: EVALUATE USING HALF-ANGLE SUBSTITUTION dx 5 + 4 sin a A. aretan (Stan (3=) + 4 arctan +C 3 В. 2 5…

A: This question is based on indefinite integral.

Q: dy_2y 4. If tan(ry) + 5= ry then show that dr²

A: tan(xy) + 5 = xy

Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: aw and ar Q2) Find if as w = 2x + 4y - z, r+s X =r tan (s), y= sin (r - s), z=e**s.

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Q: du du 1 If u = tan show that r + J: sin 2u. %3! ar X-y

A: To show the given expression using u.

Q: cos z dz (4 + sin z)?

A: The solution of above integral is written in below steps.

Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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Q: dy if y=| cos Ode dx if y= [ cos Od0. Use the Fundamental Theorem to find 3

A: We will use newton leibniz theorem to answer the given question .

Q: T/2 1 Vi- sin z dz = 2

A: Evaluate the integral 12∫0π21-sin2x dx

Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: dw when r= 3 and s = - ar 3 if w = (x+ y + z)“, x=r-s, y= cos (r + s), z= sin (r + s). Find

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Q: Q1: show that1) d/dz [cosz] = -sin z, 2) 1+tan2 z = sec2 z

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Q: az and dy Find 1. z = 4e**3 2. z = fir 3. z = cos (x°y^)

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Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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Q: rcosA 2. r sin 0 dz dr de

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Q: ome If y tanx, prove that y"-2(y +1)(3y+1). ir If x= sect and an

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Q: 1. ( )f So y sin(ry)dydr

A: Integration of sinx is -cosx

Q: dw and ar aw Q2) Find if əs w = 2x – y? + z°, X = sin (s), y=tan (r - s), z=r e°. %3|

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Q: If y = sin(msinx) then show that (1– x)' y, – xy, + m² y =0.

A: Given: Given y=sinmsin-1x We want to show that 1-x2y2-xy1+m2y=0

Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z *

A: We have to use derivative definition.

Q: d 1+ sin z Then dz cos z 1+ sin z If f(z) = cos z sec z (1+ tan z) F

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Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

Q: Qq / show thot ifa is a constont then, u(X,t) = sin lat) cos (x) is a solution to

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) * 1+tan2 z = sec2 z

A: In both solutions i have used the definition

Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

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Q: dy If tan y = X, then dis %3D

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Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: az az and du #6. Use the Chain Rule to determine given that av z = x sin (y? – x) x = 3u – v?, y =…

A: Solution:-

Q: 01. If w f(u, v), u = cosx and v = sinx, show that: d'w dx2 = v? fuu + u? frv - 2uvfur - ufu - vf,

A: Given w=f(u,v), u=cos x and v=sin xso we see that dudx=-sin x =-v   and dvdx=cos x=u.By chain rule,…

Q: az az Let z = sin(x? - y²), show that x y = 0. %3D %3D ax ay

A: Given function is  z=sinx2-y2

Q: Find ∂w/∂r and ∂w/∂s when r = π and s = 0 if w = sin (2x - y), x = r + sin s, y = rs.

A: Given w = sin (2x - y), x = r + sin s, y = rs

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: Evaluate: sin z dz +(°z – z)

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Q: I sin(z) cos(z) da : Hint:

A: Given integration is, ∫xsin(x)cos(x)dx We know that, 2sin(x)cos(x)=sin(2x) Now, the integration…

Q: Q4 Find az when u = 0,v = 0 du If z = sin xy + xsiny, x = u2 + v² ,y = uv

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Q: Q1: show that1) d/dz [cosz] = -sin z , 2) 1+tan2 z = sec2 z

A: (1) Use the first principle to derive the derivative of cos(z),…

Q: az dz A. If Z = ey sin + ex cos then show that x + y ax = 0 dy B. If f = x?cosy + y²sinx then show…

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Q: dy _ 2y 4. If tan(ry) + 5= ry then show that dr?

A: We have to do differentiate with respect to x.

Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: dy let y = (z sin z)² then is da

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: +z/3 + sin z dz

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Q: aw and ar aw Q2) Find if as w= 2x – y² + z², X = sin (s), y = tan (r - s), z=r e°.

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Q: A) Let w = 4x2 +4y² + z?, x = p sin o cos e, y = p sin o sin 0, z = pcos o. Find aw/ap, aw/a6, and…

A: "Since you asked multiple questions we will solve the first question for you. To get any specific…

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

A: