1 If g(x) = [** sec(t³) dt, then g'(x) = x O-3x² sec(x³) – sec(x³) — sec(1) tan(1) + sec(x³) tan(x³) sec(x³) O sec(1) – sec(x³)
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- sc(x) – 1 sec(x) Differentiate: f (x) = A f'(x) = - csc2(x)+ sin(x) B f'(x) = - csc²(x) – cos(x) Of(x) =cos(x)– sec2(x) (D f (x) = sin(x) – sec²(x)Find the derivative of the function f(x) = 8x – 14c by the definition of derivatives f(x +h) – f(x) h f'(x) = lim h-0 O 16x O 8x + 14 O 16x + 14 O 16x – 14 O 8xWhich of the following statements is TRUE by the Comparison Test? Hint: When x > e we have In(x) > 1. We know -1 ≤ cos(x) ≤ 1. ∞0 dx x² ln x S e10 of H e10 x p T In x e10 COS X x COS X x ·∞0 2ª X converges, because dx diverges, because e foo Loo .∞ dx de converges, because dx converges, because x² e¹0 x² dx converges, because se foo 1 ∞ [₁ fo ro 2 - 10 X de diverges. 1 x² 1 - converges. x dx converges. dx diverges. de converges.
- Let f (x) Find the values for the constants in the derivatives f' (x), f"(x), f "' (x), f(4)x). = 3 sin(4x) – 4 cos(2x). f'(x) = A sin(Bx) + C cos(Dx) A = B = C = D = f"(x) = F sin(Gx) + H cos(Jx) F = G = H = J = f" (x) = K sin(Lx) + M cos(Nx) K = %3D L = M = N = F(4)(x) = P sin(Qx ) + R cos(Sx) P = Q = R = S =Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x) - 1 O G(x) = sec(x) + 1 O G(x) = csc(x) + 1 G(x) = sec(x) - 1Find the derivatives of all functions (a) f(x) = In (sec 2x + tan 2x) (b) In ² + xy = 1 (c) y = (x³+3) 2-7x (d) y = (In x) e sex x χ
- Let f(x) = -3x" cos(x) f' (x) =Let f (x) = 3 sin(2x) – 3 cos(3x). Find the values for the constants in the derivatives f' (x), f " (x), f "'' (x), f (4)x). f'(x) = A sin(Bx) + C cos(Dx) A = B = C = D = f" (x) = F sin(Gx) + H cos(Jx) F = G = H = ] = f '' (x) = K sin(Lx) + M cos(Nx) K = L = M = N = f(4)(x) = P sin(Qx ) + R cos(Sx) P Q = R S = I| || ||If f(x) = sinx and g(x) = cosx, then what is the relation between g'(x) and f''(x)?