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

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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)…

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Q: csc(x) – 1 sec(x) Differentiate: f (x) = (A f'(x) = - csc²(x)+ sin(x) B B f'(x) = - csc2(x) – cos(x)…

A: We can use differentiation of trigonometric function rules to find the derivative of the given…

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…

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Q: I need f(1), f'(1), f"(1) Please and thank you

A: Consider the function,

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: 5. Use the chain rule to compute the derivatives. a) f(x) = sin²x = (sin x)² b) f(x) = sin(x²) c)…

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Q: Let f(x) = Then f'(x) = π The equation of the tangent line to y = f(x) at a = can be written in the…

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Q: Q5) Find f) if you know that g(x)= cos(x - 1), f) 3tan(x) at x-2

A: Given: fx=3tanx2, gx=cosx2-1 For finding ffx, we put fx in place of x in given fx

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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) ©…

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

Q: If f(x) = cos-(r"), then f'(x) = (A) (B) (C) (D) (E) -32? sin-(æ³) (A) O (B) o (c) O (D) (E)

A: We have to find derivative

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Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: 3-f(x) = tanh¯1(cos(e*))

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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: Let h(x) tan(5x + 7). Then %3D h'(4) is and h''(4) is

A: As in question it is not mentioned wheather we have to considered degree or in radian inside…

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

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Q: Determine f(x) a. f(x) = 4 sin² (x - 2) b. f(x) = 2(cos x)(sec² x)

A: (a) The given function is f(x)=4sin2x-2 Find the first derivative…

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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: 1. ſ X (2x-5)² (3-4x) dx.

A: Solution: ∫x(2x-5)2(3-4x)dx Take the partial fraction ∫398(2x-5)-514(2x-5)2-349(4x-3)dx

Q: Let f(x) = 6 sin ¹(x²). Then f'(x) equals 12x √1-x² 1 1- x4 6 /1-x² 12x cos−¹(x²) 12x √1 x4

A: The objective is to find the derivative of f(x).

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

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Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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