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x + cos(3x) f(x) = sin(tan( p sin(x))) f(x) = etan(x3) + ln(sin(. / x)). Use Logarithmic Differentiation to find the following derivatives with respect to x ... Jan 18, 2021 ... sin3x = cos(3x – 45°) ⇒ cos(90° – 3x) = cos(3x – 45°) ⇒ 90° – 3x = 3x – 45° ⇒ 6x = 135° ⇒ Ex 5.7, 7 Find the second order derivatives of the function e^6x cos⁡3x Let y = e^6x cos⁡3x Differentiating w.r.t.x . dy/dx = (d(e^6x " " cos⁡3x))/dx dy/dx ... ... (cos(x) In (wing)) dx. 1'(x)=-mi(3x) - 3. In (mix) + cos(3x). (3x).3. fox. +63(3X) cos x. Sari X. (6713x)) co>x. SmiX. (s) (3X). (smi x. 3 . (sm (3x)) In (smix) ... cos (ax+b) dx e.g. √(3x=2x) cos (3x) dx. Special Cases. x²=2x+3 sinx) (sinx) ... +3=x -3x. S. 1+x². (4-1) dx = √(u. и du dx. =2x = d₂ = du. 2x du. = 24. Sudu. esin 3x cos 3x dx = 1. 3 esin 3x + C. 53. Z e7x e7x + 5 dx = 1. 7 ln(e7x + 5) + C. 54. Z tan x dx = Z sin x cos x dx. Using the substitution u = cos x, we see ... ... cos(3x)°. What is the value of x? 1) 10. 2) 15. 3) 20. 4) 25. 19 If sin(2x + 7)° = cos(4x − 7)°, what is the value of x? 1) 7. 2) 15. 3) 21. 4) 30. 20 If sin(3x ... M(x) = e2x cos 3x sin 3x. - sin 3x cos 3x. & Y = M(x)C = e2x c1 cos 3x. - sin 3x. + c2 sin 3x cos 3x. (b) Find the solution of the initial value problem. M(0)C ... < Sux, cos 3x >. = -H. This stooks that as 3+. =0. 0 other. Fucher in V. F(I = 6) ... cos 3x unti. Vo es x)dx = 0. Page 2. (iv) the. ORTHOGONAL PROJECTION. PCA ... Feb 18, 2017 ... Explanation: Note that cos3x can be rewritten as cos(2x+x) . ... Now use cos(A+B)=cosAcosB−sinAsinB . ... Apply cos2x=2cos2x−1 and sin2x=2sinxcosx .