Solve the following items: A) Knowing that h(x) = cos(2x) * ln(1 + sin(x)), determine h'(0) B) Knowing that m(x)= x^cos(3x), determine m'(pi/3)

Q: Find f. f ''(?) = sin(?) + cos(?),    f(0) = 4,    f '(0) = 2

A: f''(x)= sin(x) + cos(x) , f(0)=4 ,f'(0) = 2

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: Given f''(x) = - 36 sin(6x) and f'(0) = 6 and f(0) = 0. 70 Find f)

A: Given that      f"(x)= -36sin(6x) , f'(0)=6 and f(0)=0 .

Q: If f(x) = sin(x³), find f'(x). 3x² cos(x³) Find f'(2). ४ OF

A:

Q: f(x) = cos(2x), then f'''(pi/4)

A: Given function is fx=cos2x.

Q: Express (cos(20)+i sin(20))*in exponential form

A:

Q: Differentiate f (x) = cos (In x) e“.

A:

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

A: Given that        f"( θ) = sin(θ)+cos(θ)  The initial condition is f(0)=5 and f'(0)=2 We have to…

Q: Given f'(x) = 6 cos x - 10 sinx and f(0) = -5, O find f(x) C

A:

Q: Find f'(x) where f(x) sin(cos(4x2 +1))

A: Consider the given function

Q: If g(x) = cos(x) then g'(x) = = g'(1) = -sin(x)

A: NOTE: Refresh your page if you can't see any equations. . take derivative…

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

A:

Q: (7) Find if \.Y =ln12- Cosx) , 2- Y= %3D

A: Calculate dydx. 1. y=ln 2-cos x. Derivate with respect to x by applying chain rule: dydx=dydududx.…

Q: Given f''(x) = - 25 sin(5x) and f'(0) = 2 and f(0) = -6. Find f() =

A: In this question, we want to compute the value of f at the given point.

Q: Given f’(x)= 3 cos x - 9 sin x and f(0)= -6 find f(x)

A: We can solve this as follows:

Q: If f(x) = 6x + 3 sin x + 3 cos x, then f'(x) = parost bundredth ) and f'(4) = (Round

A: w

Q: If f(x) = 4x(sin x + cos x), find f'(x) = f'(4) = -12 sin (4) + 20 cos (4) 0

A: given function

Q: Find (5 cos(x) + 6 sec²(x)) dx (5 cos(x) + 6 sec²(x)) dx = +C

A: Integration

Q: If f(x) = 7 sin - (2²), then f' (æ) =

A: We know , d/dx (arcsin(x))= 1/√(1-x²)

Q: Given f''(x) = – 36 sin(6x) and ƒ'(0) = 6 and ƒ(0) = 2. Find f ƒ( 5 ) =

A: