z" +7.84x = 5 cos(3t), (0) = r'(0) = 0

Q: Find f. f"(x) = cos(x), f(0) = 3, f'(0) = 6, f"(0) = 4

A:

Q: Differentiate. f(0) = 0 cos(0) sin(0)

A:

Q: (6) [²/2 sin² (2) cos2 (x).dx = A) 플 B) 플 C) 미플

A: We need to make it proper to solve this integration.

Q: Find f. f"(x) = cos(x), f(0) = 6, f'(0) = 4, f"(0) = 9 f(x) =

A: We can find the value of f(x) as below.

Q: Find dy/dx for x*+siny = x'y

A:

Q: +3x2 B) Find dy/dx if : (****")) (v)² = sin (cos³

A: Differentiation chain rule

Q: Find f. f "(x) = 7 + cos(x), f(0) = -1, f(71/2) = 0 %3D %3D

A:

Q: (10) y = एस COS (5x) ) y' = ?

A: By applying the product rule for the differentiation.

Q: Find f. f"(0) = sin(0) + cos(0), f(0) = 3, f'(0) = 4 f(0) =

A: Objective is to find f.

Q: If y = -cos(2t), then y(5)= ?

A:

Q: find y'. (show all the steps please) cos(xy) = x-y^2

A:

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

A:

Q: /2 3 d.x 2 cos x +1 -7/3

A: Given, ∫-π3π232cosx+1dx We have to evaluate the definite integral.

Q: y" - y' - y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: Given :y''-y'-y=cos5t-sin5ty(0)=2 and y'(0)=5

Q: If f(x) = 5 sin−¹(x³), find ƒ'(x). 15x² cos(x³) sin(2³)² x3 Find f'(0.4). X

A:

Q: Find f. f"(x) = 5 + cos(x), f(0) = -1, f(9π/2) = 0

A:

Q: Using Variation of Parameters 4y''-4=cos-1x

A: Given that, 4y''-4=cos-1x Now let's take, 4y''-4=0 Take m=ddx, 4m2-4y=04m2-4=0m=±1 So the homogenous…

Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: Find y'. sin t y = 8 + t %3D y' = %3D Find y'. 2 sin 0 + 9 cos 0 y = %3D sin 0 – cos 0 y' = %3D

A:

Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: let y=[cos(2x-π)]3 Find y' at x=(π/6)

A: Compute the derivative as follows.

Q: Find f. f"(e) = sin(e) + cos(8), f(0) = 2, f(0) = 2 f(e) =

A: Given problem:- f''(θ) = sin(θ) + cos(θ) , f(0) =2 , f'(0) =2  To find:- f(θ)

Q: 3 sin x 1. S- dx 1+cosx

A:

Q: Find f. f '(x) = cos(x), f(0) = 6, f '(0) = 3, f "(0) = 5

A: Differential equation: f'''(x)=cosx f(0)=6, f'(0)=3 f''(0)=5

Q: cos²od0 1. S sin*0 2. S(e-t + e')²dt

A:

Q: Find f. f(0) = f"(0) = sin(0) + cos(8), cos(8), f(0) = 1, f '(0) = 3

A:

Q: Find f. f"(8) = sin(0) + cos(8), F(0) = 5, f(0) = 4 F(8) -sin(0) – cos(0) + 5x + 6

A:

Q: 7 (1 + sin² x) = e 2" sin 2.x, y(0) = 1 X 7) dx

A: This equation solve by separation variable

Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

A:

Q: Find f. f "(0) = sin 0 + cos 0, f(0) = 1, f'(0) = 3

A:

Q: y=(b+x²)* +(1+x³)*(/3x² +x – c)cos²(4x) y' =?

A:

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

A:

Q: y" - y'-y = cos(5t)

A: Solution :-

Q: 1- 2- If x=y√√1-y², find Find y' for y=cos(sin²x) dy dx

A:

Q: Find f. f "(e) = sin(e) + cos(e), f(0) = 5, f (0) = 4 f(e)

A: Just use the basic integration of trigonometric and then find the value of integration constant from…