If f(2010) = π/2, f(2x) = f(x)Vx E R and f(x) is continuous for x E R, then the value of cos(f(x))-cos(f(x)) sin²x limx→ (A) 1/4 is Limx→n/2 (B) 1 TT- COSX (C) 0 (D) None of these

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

A: We have to find

Q: Let f(x) = 3 cos a - 2 tan a f'(x) = r() - C f'

A:

Q: Evaluate 1 70 sin° (f (x)) cos*(f (x))g(x) dx COS where g'(x) = r for all x with g(0) = T , • f'(x)…

A:

Q: Let f(æ) = sin(x) and g(æ) = x² . Find (go f)'(x) O 2sin(x)cos(x) O 2xcos(x?) -2æcos(x?) 2xcos(x)

A: Given that f(x)= sinx and g(x)=x2. And we find (g0f)'(x). We know that d(xn)/dx = nxn-1.     Here i…

Q: Find f(x).

A: Given,

Q: If f( x ) = sin (x) – e“ , what is f'(x) ? O f'(x)=- cos(x)-e² — сos(2) —е* O f'(x)=sin (x) –e² O f…

A:

Q: If f(x) = cos(x) +3z³, what is f'(æ)? O f'(x) = sin(x) +3z³ O f'(x) = sin(x)+ 9x² O f'(x) =…

A:

Q: Suppose (=/3) = 3 and f '(m/3) = -7, and let g(x) = f(x) sinx and h(x) = (cos x)/(x). Find the…

A: So, Again, if , Then

Q: Let f(x) = sin(2x) + cos(x) then f"(x) Select one: O a. 4sin(2z) + cos(z) O b. -sin(2x) – cos(x) Oc…

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Q: cos(x) Find g' (x) f(x) and let g (x) :

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Q: Find for f'(x) | f(x) = x – cos(x) f(x) = e* – 2x - 2

A: To find f'(x).

Q: Suppose f(x) = 3*sec(3*) tan( 3*). Evaluate: / s(x)dx sec(3*) A +C In (3) 3*. sec(3*) +C B In (3) ©…

A:

Q: Let f"(x) = x'/A cos(x), /(0) = 2, and f(1) = 2. Is it true or false that 7=-73+ cos(x) + 28…

A: The answer of above solution is option A. i.e true.

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: Let ƒ(x) = (cos( − 4x – 5)) (sin(6x − 2)). Then ƒ'(x) =

A: f(x)=(cos(-4x-5))(sin(6x-2))

Q: If V(x)= In[sin(x)- cot(x)], find V'(x). %3D O a. cos(x)- csc-(x) sin(x) + cot(x) O b. cos(x)-…

A: Here we have, V(x)=lnsin(x)-cot(x) We have to find V'(x)=?

Q: If f(x) = x² + cos(x), what is f" (x)?

A:

Q: cos x tan x a) lim x→0 2x (x2 b) lim sin(x-) 4 x- 4

A:

Q: If g(x) = 3 sin x + 2 cos x + 5, then g' (3) = A B 12/3-√3 - 3/2+√3

A:

Q: Find g'(x) given that g(x) = x° cos(Tx) os (πα)

A: Given,  g(x)=x3cos(πx)

Q: Find f'(x) if f(x) = tan-1 2x sec²(x) 1 1+x² 2x 1+x² 2x 1+x¹ 2x 1+x² 1-¹ (x²).

A:

Q: (x) = [*cos(t¹) dt, then g'(x) cos(x7) — sin(x7) — sin(77) + sin(x²) cos(77) - cos(x7)

A: Given query is to find the derivative.

Q: 2. Find the derivative of each of the following: (a) f(x)= 3" cos² (}x) %3D (b) h(x) = Vrd – 4x + 1…

A: (a) Consider the given function, fx=3xcos212x Here the objective is to find the derivative of the…

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: If f(x) = 7cos(x), what is f'(x) ?

A:

Q: If f(x)=sin(sin x) then f'(0) is .. Jika f(x)=sin(sin x) maka f'(0) adalah ... 1. O -1 2. O 1 3. O 0…

A:

Q: Let g(x) - S²³ = 2 sin(t)e dt. Then g'(x) equals

A: Here for given g(x) we have to find g'(x)

Q: Consider the following function: - {% f(x) = x0 Select the item below that correctly describes the…

A:

Q: 1+cosx Show that if f(x) = In| then f'(x) = -cscx. %3D 1-cosx

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Q: Q1) find dy/dx 1) F(x) = sin’2x tan x² x – 3 ) 2) F(x) = sin( x +4

A:

Q: Find f if f"(x) =2 + cos(x), f(0) = 10, f(t/2) = -5. f(x) = |

A: To find f if f"x=2+cosx, f0=10, fπ2=-5. Solution: We have, f"x=2+cosx Integrating both sides, we get…

Q: Let f(æ) -4 cos x + 8 tan x f'(x) = r(#) - 27 f' 3

A: