Find y'' if y = 6x sin x. A. y' = 6 cos x - 12x sinx B. y'= - 12 cos x + 6x sin x C. y' = 12 cos x - 6x sin x D. y'= -6x sin x

Q: Find h'(x) if h (x) (2 csc x) (5 sin x - 3x). O-2 cot2 x (5 sin x - 3x) O2 cotx (5 cotx - csc x) -2…

A: Givenhx=2cscx5sinx-3x We know that cscx=1sinx We know that dcscxdx=-cscx.cotx Product rule for…

Q: y' + y tan x = sin 2x cos³ x y3 given x=0, y=1

A:

Q: y'tan x sin 2y = sin² x + cos² y.

A: We need to solve y' tanx sin2y=sin2x+cos2y This can be written as: y' tanx…

Q: Find the value →21. csc (sec- 2) + cos (tan¬1 (– V3))

A:

Q: sin (Vx).cos (Vx) dx = ?

A:

Q: Find y ' if sin (x+ y ) = y 2   cos x

A:

Q: g(x) = 4ecoN " sin x, (0, ] COS

A: Given data:   The given function is: g(x)=4ecosxsinx The given interval is: [a,b]=[0,π].   The…

Q: If f(x) = = sin (3 – x), then f'(0) O 6 sin 3 cos 3 O 6 cos 3 O -2 sin 3 cos 3 O -2 cos 3 -2 cos O 2…

A: f(x)=sin2(3-x)

Q: 5. y = 5 tan x³ + sec (3x)

A: Topic = Derivative

Q: Let f(x) - 6 cos 6 cos° x f '(x) =

A:

Q: Differentiate y = In ( sin² (4x)). A y' = 8 tan (4x) y' = 8 cot (4x) y' = 8 csc2 (4x) sin (8x) y' =…

A:

Q: (sin-'(cos(2x) + cos-'(sin(2x).

A: Given : ddxsin-1cos2x+cos-1sin2x

Q: (a) [- 9x2 +x° cos x dx = 3

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: | 1' cos(T +1) dr. COS

A: using the integration by parts

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 y' if 4 cos x cos y = 3y. %3D

A: To find the derivative.

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

A:

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

A:

Q: sin x = csc 2x cos x cos 3x sec 2x

A:

Q: Given f'"(1) = – 4 sin(2x) and f'(0) = 2 and f(0) = 1. Find fG): sin(7 + 1)

A:

Q: x" - x' - 2x = sin3t

A: Consider the given differential equation, x''-x'-2x=sin3t make the auxiliary equation,…

Q: What is the derivative of y = 3x6? 2x6 2x5 18x6 18x5

A:

Q: Find y' of tan x = Sin y -2x5

A:

Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: Cos (-x)= - Cosx

A: Let, cos-1(-x)=yThen,-x=cosyx=-cosy

Q: Solve y'-y cosx = cos x

A: We now solve the differential equation, y' -ycosx=cosx . This is a first order homogeneous equation.