Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0) = f(x), - 00 X> 00 - ot

Q: If f(x)=2 sin x/1+cos x, then f′(x) =    f′(4) =

A: We have to find

Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: 3. Find f. (a) f"(x) = x + 12x² %3D

A:

Q: 3. (a) (10) Let g(x) Find g'(x). Don't try to simplify your answer. In(4.x) – cos(2x)

A: Given function g(x) is differentiate w.r.t x as written below:

Q: f(x) = 3x cos ƒ'(x). -1 (2x + 4) − √√/19 − 3x², find

A: Given: fx=3xcos-12x+4-19-3x2. To Find: f'x.

Q: The function f(x) = a sin x + b cos x + c satisfies f"(x) = cos x – 2 sin x, f'(0) = f(0) = 2. Find…

A: a=2 b=-1 c=3

Q: Compute the derivative of f(x) = ( sin(2x + 1))/°. 4 (sin(2x+ 3 1) -1/3 • cos (2x + 1) 4 -1/3…

A: Given

Q: Find f. f(x) = f"(x) = cos(x), f(0) = 9, f'(0): = = 8, f "(0) = 6

A: Given,  f'''(x)=cosx, f(0)=9, f'(0)=8, f''(0)=6

Q: (a) Let f(x) = (3x – 7) *". Find f2®(x). 49 (b) Let g(x) = cos(9x +2). Find gº" (34) '(x).

A: Consider the part (a): Consider the following function: fx=3x-749…

Q: Solve sin (x) + sin(x) = 0 on [0, 27]

A:

Q: Find f. f"(x) = 5e* – 8 sin(x), f(0) = 3, = 0 %3D %3D f(x) = IN

A: Answer and explanation is given below

Q: on Find an equation for the function f(x) whose derivative is f'(x) = 4sin(8x) and whose graph…

A:

Q: Let Find f(x) = y = f(x) = 5x + 18 cos x. d f(x) =

A: Given query is to find the derivative at indicated point.

Q: Let f(x) = cos(x). (a) On [0,2n) solve f(x) = 0. 4.

A:

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: Find f. f(x) = f"(x) = x3 + sinh(x), f(0) = 1, f(2) = 2.6 ×

A:

Q: = 4 and f Find the following. Suppose f 3. -5. Let g(x) = f(x) sin(x) and h(x) = f(x) 3 (a) g 3…

A:

Q: Find f. f "(x) = 5 + cos(x), f(0) = –1, f(9/2) = 0 f(x) : %D

A:

Q: Find f if f'(x) = 2 + cos(x), ƒ(0) = 10, ƒ(π/2) = 6. 2 f(x) = x² − cos(x) – (n - + - (x + 10 ) x +…

A:

Q: by s- differentiation find L(te-3t) = 1 .aO (s- 3) 1 .b O (s-3)2 (s+3) .dO (s+3) 2 1.

A: The solution is given as

Q: If f(x)=2x-3, and g(x) is a function such that g"(0) = 4 and (fg)"(0) = -4, then g'(0) =

A:

Q: x2 - 2x + 3, x<0 cos를+2. + 2, COS Evaluate f'(-2) and 4.

A: It is given that,       fx=34x2-2x+3 , x&lt;0cosx2+2 , x≥0 Evaluate f'(-2).

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.