Let x² + sin(yz) = xz² + y dz and ду dz Find

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

A:

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: Find dy/dx  if  4 cosx siny = 1

A: We will directly differentiate it.

Q: 1 If z = 2x2 – 3y with u = x² sin y and v = 2y cos x, determine expressions %3D az dz for and du

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Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Differentiate y = In (sin + cos ) cos -sin 2r Va(sin a + cos V") sin E + cos E 2r V(sin a + cos a)…

A: we will apply, chain rule: ddxf(g(x))=ddg(x)(f(g(x)))×ddx(g(x)) Sum rule:…

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: Calculate for w-z sin(xy+).

A: The given function is w=zsinxy4+9z

Q: 3+2cosx dx is equal to (2+3cosx) sin x 2 cosx 2+3cos x) 2+3sin x 2 cos x 2 sin x (d) 2+3cosx 2+3sin…

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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Q: 1- d/dz [cosz] = -sin z

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Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: I. Find dy -and simplify the result whenever possik dx 1. у%3Dsec3 2х - 3sec2x 2. y = sin (x + 4 )…

A: Given; 2) y=sin(x+4) cos(x-4) 3) y= -3 cot5(x/3)/5 + cot3(x/3) -3cot(x/3) - x.

Q: Show that : y' = 1 when y(x) = sin-(x) %3D V1– x2

A: Differentiation is done in many ways. Some of the rules of differentiation are illustrated below :…

Q: (b) Show that 1 2t and sin x = cos x= 1 +? 1 + ? (c) Show that dt 1 + f dx %3D 2.

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Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: cosxdx 17. - secx+ tan x [2sin(3x)cos(5x)dx 18. [(sin y +2cos y)'dy 19. 20. ſcot'(2x)dx 21. (sin“…

A: solution is given below

Q: If we have to check the DE sin(x). dy +y cos(x) = 1 dx for Exact then My = - sin(x) -sin(x) -cos(x)…

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: evaluate  0∫π 0∫1 1/6∫1/2 xy sin z dxdydz

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Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

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Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: Find , where : = sin (a²) cos (y*) O 2.r sin (a²) cos (y²) O 2r sin (x²) 6.x sin (a²) cos (y²) 2x…

A: We have to find partial derivative of z  with respect to x.Given a function of two variables, ƒ ( x,…

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

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: b) Is S cos4xv2 – sin4x dx = V(2 – sin4x)³ + C true or false? show me %3D

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Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: Differentiate y= cos y2x +1 sin 2x+1 A. V2x+1 sin 2x+1 B. V2x+1 sin 2x+1 C. V2x-1 sin 2x-1 D. V2x+1

A: Please refer the attached image for complete solution. THANK YOU.

Q: y'' + 3y' + 2y = sin ex

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: vE zy sin{z° + y)dzdy Find

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Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: 1. Find y" when sinx + siny = 1.

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

A: The question is of change of order. First we need to identify the region formed by limits of…

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: 12) / Зy sin(5y?) dy

A: Solution:

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

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Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: sin³€ dt to ylomeldon 3.

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Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2>0 then…

Q: find tan x dx x² x² tan¬' x dx 19. 20. sin 3x cos 2x dx 22. sin 2x cos 3x dx S sin sin 8 sin 4t sin…

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Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

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Q: Verify that sin(x+y)+sin(x-y)=2sinxcosy

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.