f(t) = 3 sinh(2t) + 3 sin(2t) A) F(s) = s2-4 B) F(s) =+ s2-4 C) F(s) =+ %3D s2 +4 D) F(s) = -+ s2-4

Q: Find the derivative (df/dx) 1- f(x) = cscx - 4√x + 7y−² 2-f(x)=x² cotx-x-2 3-f(x) = (secx + tanx)…

A: We have to find derivative of given function.

Q: If f(x) = tan (3x), then f'(x) = (A) 12 tan (3x) sec?(3x) (B) 4 tan (3æ) sec2(3x) (C) 12 tan (3x)…

A: derivative

Q: (5) (sec-i x) =, d

A:

Q: 3. Solve the following equations over the interval [0, 2π]. Use exact values where possible, or…

A: a) tan2x=13 tan2x=13tan x=±13x=π6,7π6,5π6,11π6

Q: f(x) COSX f'x) 2.

A:

Q: Q3\ find General solution of sin (xy). (ydx + xdy) = 0 %3D

A:

Q: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: tan x If f(x) = 3 sec a f (2) = f (1) =

A:

Q: ことる ーx (x+2)(X-2) -6x (x -ax+4) y" CX+2) (x-1)3 need first derivative Eanalysis %3D (x-2)3 (x+2)°

A:

Q: Find the d. c. of T from definition.

A:

Q: 3. Find the derivatives: 3x3-4 a) f (x) = b) y = (x2 + 6x + 2) (+ Vx5 + 3) DO NOT SIMPLIFY 2x²+3 c)…

A: a) Use quotient rule of derivative and find the derivatives of above function.

Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: Solve: y/" – 4y" + 53y = 0 O y = C1 + C2e cos2x + C3e-7* sin2x 7x O y = C1 + C2e cos2x + C3 e7"…

A:

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: dx 1-S 1-sinx

A: “Since you have posted multiple questions, we will solve first question for you. To get remaining…

Q: cos(4x) cos(2x) sin(4x) sec(2x) 12. Verify: - sin(2x)

A: cos(2x ) =cos2(x)-sin2(x) = 2cos2(x)-1 =1-2sin2(x) sin(2x) = 2sin(x) cos(x)

Q: Find general solution of ODE   (x+y-1)dx-(x+y)dy=0 dy/dx = (x+2y-3)/(2x+y-3)

A:

Q: solve it y''+3y'+2y=cos(e

A: The given differential equation is

Q: Find f ′(a) f(t) = t^5 - 3t

A:

Q: The general solution of the equation (D*+D)y=-12 is y-+x+ccosx + c,ainx +6x ® y-c, + cx + cycosx +…

A:

Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: Solve for the general solution: (D² + 5)y=0. Oy=c1 e^(√5x) + c2 x e^(√5x) O y = c1 cos(√5x) + c2…

A:

Q: dy Find if y = 4 sin?(3x) dx

A: Here we have to find the derivative of function y which is given as above. Here I am attaching a…

Q: Compute y' for y=√(3x++ e - 3x) 8 A (В B D Say 3 24 y = ²4 (4x³ - e-³x) (3x + + e-³x) ³ 5 3 8…

A:

Q: d dx x= ||

A: Given that

Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

Q: find dy/dx x(х+1)(х- 2) (х*+1)(2х+3) 25) у%3 43) у%3D 1+(lin x)? 1+(ln x)?

A:

Q: given that the derivative of f(x)=10 5√x^3−√x^7+6 3√x^8−3 is 6x−2/5−7/2x^5/2+16x^5/3, what does 2+2…

A:

Q: The function f(x) = sin(kx) contains the point A(, -1). The function is: Oa) f(x) = sin(-x) Ob)…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.