2- X. Sin (5X) dx: Cos (SX) X Sin (SX), Cos (SX) XSin (SX) XSin (SX) Cos (SX) 25 25 25

Q: Can you help me step by step?

A: Using the formula of derivative of quotient of two functions, that is, . And using , we have,

Q: 10. [x'sin(x')dx 11. [x sin(x)dx 12. [sin(x*)dx 13. ſe* dx 14. [xe* dx 15. [cos (x)dx

A:

Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral

Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

A:

Q: Q. It sin x Cos X XCOS xQ /- sin xd 3.

A:

Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

A:

Q: 2FI 2 sin nx dx cos nx dx =0, where n integer. %3D !! 0.

A: Note: -     as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 7. f (ex + 1)² dx 8. fex dx/(e²x + 3) 9. f (cos x-sin x)² dx

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Q: 3r cos(x) 1. Evaluate dx V1+ sin(x)

A:

Q: 4 Find dx for y = - +7 sin x. X

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Q: 4. J (cos x – sin x)²dx

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Q: y = (sin x +cos x) sec x = sec² x

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Q: Determine dy/dx given that y = 1+sin x COS C 1 O (1+sin x)² -1 O 1+sin x 1 O 1+sin x -1 O (1+sin x)²

A: The objective of the question is determine the derivative of the given function and choose the…

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 4. (3sin y- 5x)dx +2x cot ydy = 0 Ans. x'(sin y-x) = csin²y

A:

Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

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Q: dy Find for y = - 7x+5 cos x. dx

A:

Q: sin x dy Given: y = Compute for dx 1-2 cos x

A: The given function is y=sin x1-2 cos x

Q: S[cos 3(x/3)]dx

A:

Q: 3. S sin x In(cos x) dx

A: According to company rule, we can answer only first question.

Q: e2x dx 1. Зе2x+1 2. sinx dx 1 3. cos 2x

A: As per bartleby guidelines we are supported to answer only first three subparts,  kindly repost…

Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

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Q: x4 1 If u = tan(- + y° x² – y² - then show that ди du + Y- ду X - = sin2u dx

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Q: dz 1) Find ifz = 3 cos x – sin(xy),x =y = 3t - dt

A: NOTE*** As per bartleby guideline for more than one question asked only first is to be answered…

Q: 3. f(x,y) tanx - sec²x - cosy

A:

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: S cos^3 (x/3) dx

A: ∫ cos3(x/3) dx ∫ cos(x/3) cos2(x/3) dx  ∫ cos(x/3) (1-sin2(x/3)) dx.         ..(1) (Beacuse…

Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

A:

Q: Take the derivative of this integral.

A: Given

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

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

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 19. i) Differentiate sinx with respect to x from first principle 1+3x dy ii) Find, dx when a) y (x…

A: Part i,Given,          fx=sinx

Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: .2. COS X sın.x.ços.Xdx

A:

Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

A:

Q: 5) Find 业一 dy for y cos(x) sin(x)

A: We have to find the first derivative.

Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: -3π/2 2. S TL √sinx + 1 cos x dx

A: We solve the given definite integral by using substitution method .

Q: 2. sin x siny dy + cos x cos y dx = x² sin x cos y dx

A:

Q: S sin x (1+ cos 2x)² dx

A: In some cases integrals can be converted to standard integrals using an appropriate substitution.…

Q: 3. sin x cos y dx + cos x sin y dy

A:

Q: 2 sinºx cos®x dx

A: here we use integration method, as we seen that the power of the sin and cos are even . so we use…

Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

A:

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Q.1\Find (1) I=S tan³(5x) sec²(5x) dx. (2) =S dx x3+2x3+1 Q.2\ Find if y = lIn sin (x) cos(x*).V1+x)…

A: As per our guidelines I am solving only first question please resubmit other questions.

Q: 4. cos x dy + y(sinx- 1) dx = 0; when x = n, y = -2

A: (4) To find: The solution of differential equation. Given: The differential equation is…

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

A:

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

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