Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: d²y If y=cos 4xr, then at x = 0 dx?

A: Given,     y=cos4x

Q: dz az C. Find ax and 4. 5x*y?z-y cos xz = 2x°+y

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Q: -3 Evaluate: ²¹²² ²³ y cos(z³) dx dy dz

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Q: dy If y= sec +cos(x), then dx Select one: -2x -2x O a. x-1 1-x ーメ 2x 2x O b. x-1 メー1 V1-メ -4x C.…

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Q: Given that 2x2 - 5y = 3xy. Find the value of dy/dx at the point (-2,2)

A: Given : 2x2 - 5y = 3xy

Q: y = C,e²x cos(3x) + C2e2x sin(3x)

A: y=c1e2xcos3x+c2e2xsin3x  differentiate with respect to x…

Q: 3) eYsinx dx = cos?x dy 4) y' + (÷) y = xy?

A: First question we can easily solve using veriable separable method. Second question we can use from…

Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: d²y dy and - dx B) Find if x = sin? 3z and y = tan 3z dx2

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Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: dy Given y=5e3 + sin x, is dx A 15e3x + cosx B B 5e3 + cosx ©5e3- cosx O 15e3 - cosx

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Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: d²y Given that y = -4x cos 2x +4 sin 2x, find dx² at x = 2

A: Given: y=-4xcos2x+4xsin2x

Q: d²y dy and dx Find if x = sin 3z and y = tan23z dx2

A: It can be observed that both the variables x and y are the functions of  z, therefore to find the…

Q: Find the solution. (Dª+2D3 + 10D2)y =0. @y = c,e-+czxe¯+e"(e,cos3r +c,sin3x) y = (c,+c,)x+e*(c,cos3x…

A: To solve the given Differential equation.

Q: 1. Given that Y = e + Cosx, find: dy a. dr b. d'y/dx?

A: Hello , thanks for your question but according to our policy I am answering the very first question…

Q: f(t) = e2t – 2t² cos 4t + 3t sin 6t – 2t + 5 %3D -

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Q: Given z 13t 9 and y- 169 sin : dy dx d²y da?

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Q: dy If y= sec +cos-1(x²), then dx Select one: -2x O a. Vx* -1 V1-x* 2x 2x 2x Ob. Vx*-1 V1-x -4x Oc.…

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Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: Q5: If y = A sin 4x then, show that d³y d'y dy dx3 + 16- dx + 16y = 0 %3D dx2

A: Topic:- application of derivatives

Q: If 3x2 +2xy +y² = 2, then the value of dy at x=1 is dx

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Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

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Q: d²y Answer: 1 . If x = t + cos t, y = sin t, find dx2 dx2 (1-sin t)

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Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: If x = t +cos t, y= sin t, find d^2/dx^2

A: Given that      x=t+cost , y=sint  Here we have to find d2y/dx2 .

Q: dy/dx = cos3x/sin2y. Given y=pie/2 when x=pie

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Q: Given that y=e3x sin 2x. Show that d2y/dx2 - 6dy/dx + 13y = 0

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Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: (b) Find, where y= cos ecx- dx -4x+7

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: If y = cos24x, find dy/dx. a. 2cos4x     b. 2sin4x c. -4sin8x    d. -8sin4x

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Q: dy 7. Find ,y = cos³xsinx? dx

A: Given: y=cos3xsinx2 Formula used: Product rule of derivative: ddxf×g=dfdx×g+dgdx×f Power rule of…

Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: The general solution of y-y=D0 is: y=ce*(c,cosx+ czsinx) -A O y=c;e*+c2e*+ c3cosx+ C4sinx BO…

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Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: Find d2y/dx2 implicitly in terms of x and y 7xy + sin x = 2

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Q: Find the solution of sin 3ædx + 2ycos³3xdy = 0 O y? = sec 3xtan 3x + C O y? = -sec 3ætan 3x + C O y?…

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Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

Q: dy Given that y =÷-sin3x . Find de 2 18. 4 +3cos 3x A B 4 -3 cos 3x 4 3 cos 3x C +3 cos 3x O A Ов

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: cos(xy) + sin(x/y) = 2y find dy/dx at point (pi,1)

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Q: ‏Solve it quickly please

A: dy/dx=(dy/dt)/(dx/dt).