Find the differential of each function. (a) y = 2 + 55 dy (5s + 2)² (b) y = eu cos(u) 1. dy = e"(sin(u) + cos(u) )

Q: (5) If y = sin(3x) the find y"

A: We have given trigonometric equation  y=sin3x y'=dydx y'=ddxsin3x y'=cos3x·ddx3x y'=3cos3x…

Q: 6. (a) cos 2x dx; u = 2x

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Q: S(;+ sin(x) – Vx²) dx

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Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: a Jx'cos(x')dr= a d. 1 sin(*) +C sin +C e -sin sin(x') +C sin(x 3 3 +C 3

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Q: (e) sin(2x) sin(x) dx.

A: ∫sin2xsinxdx

Q: Find the first and second derivatives of the function. g'(u) = g"(u) = g(u) = u(4u – 7)³ 1

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Q: 음 (sin-" (2))\_-+ = (교2)) | dx 2(:) A 1+ 2() B (C 2 (4) cos-1 (16) D -2 (금) cot () csc(6) CSC

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 1. y= ;d'y/dx 2. Y = (7x + 2)S ;y"…

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Q: 3y' –4x²y+ xy = -5 %3D

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Let h(y) = 2 cos y – 7 sin y. Then h'(y) =

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Q: dx

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Q: y+y=sin(x), where y(x) = 1.

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Q: b) Find derivative of the following: 1. y= 5x° + 2x -x + x* -9x+12 y=1-cos 20+3sine iI. ii. s= xln…

A: The detailed solution is as follows below:

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: Find the derivative of 7 (t) = (1+t°, te¯t, sin (2t)) A. F'(t) = (3t°, (1 + t)e¯t, 2 cos (2t)) B.…

A: We are asked to find the derivatives.

Q: 13. (D -1)y = x' sin 3.x

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Q: 11. y = (x + y) 12. y =x sin -1x + 1 – x2

A: Let's find.

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations