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

Differentiate the following functions

Let f(x)= f'(2π) = = - 7x sin(x) + cos(x) Evaluate f'(x) at x = 2πT.

Let f(x) = f²ª² sin t² dt. Find f'(x) 2x ○ 2x sin(x²) — 2 sin(4x²) sin(x¹) — sin(4x²) 2x cos(x¹) - 2 cos (4x²) ○ cos(x4) — cos(4x²)

Let h(x) = 8(x) f(x) If f (x) = cos (x) and g(x) = 4x² + 2x – 3, what is h' (x)?

i) Let f(r) = e2-g(x) where g(2) = -1 and g'(2) = 7, and g"(2) to calculate f"(2). Show your work. 3. = -4. Use the product rule twice Hint. e2 = (e")2. ii) Let F(x) = f(xf(rf(x))) where f(1) = 2, f(2) = 3, f'(1) = 4, f'(2) = 5, and f'(3) = 6. Calculate F'(1). Show your work.

If f(x) = f'(x) = ƒ'(3) = 4 sin x 1 + cos x 4 1+ cos os(2) then

1) Let f(x) = sin² (3x4). Derive the derivative f'(x). Choose the best answer. O 24x^3sin(3x^4)cos(12x^3) O 12xsin(3x^4)cos(3x^4) O 12xsin(3x^4)cos(12x^3) None of these are correct. O 24x^3 sin(3x^4)cos(3x^4)