Determine of y = cos(x) – V5a2 In x.

Q: Eliminate the arbitrary constant/s: y = C1e^ax cosbx + C2e^ax sinbx where a and b are parameters (…

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Q: J cos 2x sin 3x dx

A: To find: The integral of ∫cos2x·sin3xdx. Formula used: Trigonometric formula: 2cosA·sin…

Q: Differentiate. y =  emx Cos nx

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Q: e) у- In 2 2xe dx 1 dx xcos(In x) /2 g) y= V1+cos4xdx

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Q: Differentiate y with respect to x where y= cos(-3x2)

A: Differentiate y with respect to x.

Q: y' – 3y + 2y = cos(e-")

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Q: find dy/dx. y = -10x + 3 cos x

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Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: J cos 3x cos 4x dx :

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Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

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Q: Differentiate : a. y= 9x sec (x/3) b. y= sin2x/1-cos2x

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Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: y 2sin x-cos 2.x for 0° sxs360

A: Consider the function, y=2sinx-cos2x Differentiate with respect of x,…

Q: Find the general solution of y'= sin²xcosy.

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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: Find y' : In(cos² 3x) = e*+y + sin-1 y

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Q: dy Cos(3x) + (In x)

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Q: x fare cos = dx 2

A: Indefinite Integration

Q: 5. J sinx cos²x dx V1 − cosx -

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: V3x d. Evaluate dx sin(3t) dt

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Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: S2ta J 2tan x In (cos x) dx=

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Q: find dy. = cos (x2)

A: Given- y=cosx2 To find- The value of dydx. Formula used- ddxcosx=-sinx.

Q: Find the general solution for (cosx)y' = 1 – y² consider y, (x) = sinx. %3D

A: Given:  cosxy'=1-y2                  1          , y1x=sinx Let y=y1+u be a solution of (1)…

Q: Find if y%3D cos (2x)+ 2еж: dx dy

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Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: Find dy/dx for 4 cos4 xsiny = 15

A: d(uv)dx=udvdx+dudxv

Q: ution of y" + 4y = cos 2x b

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Q: Evaluate J2 e* cosx dx 0.

A: To evaluate: The definite integral ∫0π2ex·cos x·dx. Concept used: Integration by parts:…

Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to…

Q: 125. y = / V2 + cos³t dt

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: Intergrate dy (2y-x) =In Co)

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Q: y" – 3y' + 2y = cos(e-*)

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Q: if  x²v+sin(xu)-yv²+u³v=1 x²u-2yv=1 ، cos(xu)+yv=5  ,find dy/dx

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Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: Find the value of zr» at the point (0, 3, 2) where a²y² + 2² – cos(ryz) = 10.

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Q: 2-€2x y") edxtcuxe yd-siny)lye.co

A: A differential equation of type   P(x,y)dx+Q(x,y)dy=0   is called an exact differential…

Q: find the differential dy of the function y=x2sin(8x)

A: Find the differential dy of the function y = x2 sin(8x) as follows.

Q: (b) Determine cos(x²) 2x dx by using substitution method.

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Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: 2. sin3x dx + 2y cos³3x dy = 0

A: Given- sin3xdx+2ycos33xdy=0 To Solve- The above differential equation.

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below