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

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

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

A: Given,     y=cos4x

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

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Q: dy 7. dx cos(x + y), when x = 0,y = 4

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Q: Q) Lind d/dx of ® xe 1o x+3J = 0 2 2sinx cos y =1 ® x -se cs

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Q: dy A. Find for the following: dx (5+ sech(5x) 3/2 iv. y = x3 у %3D (1+ sinx)(х — х3) V.

A: iv.

Q: dy Find dx 2x %3D sin (x + 9y)

A: Given that e2x=sin (x+9y) Chain rule: If a function y=f(x)=g(u) and if u=h(x), then the chain rule…

Q: 2FI 2FI sım nx dx = cos nx dx = 0, where n integer. 0.-

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Q: dy given that In(x + y2)-tan-1 31) Find = 0. dx

A: Given: lnx2+y2-tan-1yx=0 To Find: dydx=?

Q: S V3x – I dx а. - b. f cos 7x dx J 2+sin x COS x dx с.

A: As per our guidelines we are supposed to answer only three subparts of a question. Kindly repost…

Q: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

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Q: Q2/Find dx of y = sin(e') + xtan-1x. %3D

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Q: Find dy/dx for the fo d) x' + x.tan y = y -1

A: There are multiple question, As per our company policy ask other question separately. d.

Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

A: I am attaching image so that you understand each and every step.

Q: b. sin 2xdy – 2(y - cosx)dx = 0; when x = 1/4, y = 0

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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: dy at the given point. dx Calculate sin² (–5y) = x + y, - %3D 4

A: Given equation sin2(-5y)=x+y and point 2-π4,π4 The objective is to calculatedydx at the point.

Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: dy Find for y = sin (2x +3) da %3D Ans=

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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: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: - (2y cosx + sin* x)dx : sin x dy, when x =y= 1 %3D

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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: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

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Q: d?y dy 20. 4 + 4y = 2e2x – 12 cos 3x - 5 sin 3x, at y(0) = -2 and y(0) = 4 dx2

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Q: dy 4 sin 2x, y = 2, when x = 1/2 dx

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Q: dy Find dx for y = 14x +5 coS x. d(14x+5 cos x)%3D

A: Formulas:1. ddxxn = nxn-12. ddxcosx = -sinx

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

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Q: dy Find for y = cosx(1 + cscx) dx %3D

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Q: Find dy : (a) y = cos(1 Ix + 5x) dx

A: Topic:- calculus

Q: dy Find dx 1-4x V1+4x (a) y= cos'(sinx) (b) y = = arctan

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Q: dy Find dx y = = 5x° sin x coS X

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Q: Use this equation to find dy/dx. 4y cos(x) = x² + y2

A: We will differentiate  equation with respect to X.

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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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: dy for y=In (x² +1}+ (sin x +5)*. Find dx

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Q: Chose only two: dy 1. Find for y + In x2 y2 -cos 2x* = 27 dx 2x+1 2. Evaluate: f dx -4

A: We use chain rule and product rule while differentiating the given equation.  Also for integration,…

Q: Find dy/dx: (a). y = cos 8x + sin r2, (b). y = Vcos 8x + sin x². %3D

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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: 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: (D² – 3D + 2) y = 14 sin 2x – 18 cos 2x

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Q: dz Find dy x² sin(2y 5z) = 1+ y cos(6za)

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Q: Find dy dx the function y=2 sin 3X cos 2X

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Q: Use this equation to find dy/dx. 8y cos(x) = x2 + y2 dy dx II

A: Given  8y cos(x)=x2+y2We find dydx

Q: Find dY for the function y= cos² 3X+ VSin x dx

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Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: dy No need to simplify. А. Find dx 1. y = cos 3x 2. y = tan? | 3x² 3. y = 5x$ 13

A: We know that  ddxcosax+b= -sinax+bddxax+b ddxtan fx = sec2fxddxfx and ddxxn=nxn-1

Q: Ql find dy 2メ for y= cos ( Inx + e %3D dx

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Q: dy dx 2. 2X for y = cos (Inx + e) %3D

A: ddx(Cos(x)) = -sin(x)ddxex =exddx(log(x)) =1xddxxn=nxn-1Chain ruleddxf(f(x)) =f'(f'(x)) Here , In…