# SOLUTION: Hello all! I have this Trigonometry homework that is killing me and I need help from you guy's. Here's the problem let me know if you guys can solve it. 1. Calculate the der

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Hello all! I have this Trigonometry homework that is killing me and I need help from you guy's. Here's the problem let me know if you guys can solve it. 1. Calculate the der      Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Trigonometry-basics Question 167547: Hello all! I have this Trigonometry homework that is killing me and I need help from you guy's. Here's the problem let me know if you guys can solve it. 1. Calculate the derivatives: I) I) (Sin4x) /( x² +1) II) II) 10t²+1 III) III) √ ( 1 + u) / (1 – u) IV) IV) (1) / ( x­­­­­­­4 + 1)3 2. Calculate the points of the tangent of the curve : y = ex(x2 – 8) where and in which the tangent line is horizontal 3. Write one of the two tangents to the curve : y = 1 + x³ which are parallel to this equation 12x - y = 1. 4. Calculate I) If f(x) = ex cos x calculate f ’(x) et f ’’ (ii) Calculate (d99/ dx99) Sin x 5. Calculate the derivative : I) y = xe-x² II) Let say: r(x) = f(g(h(x))) whit h(1) = 2, g(2) = 3, h’(1)= 4, g’(2) = 5, f’(3) = 6. Calculate r’(1). III) Show that the function : y = Ae-x + Be-x satisfy the equation with differential y”+ 2y’+y = 0Answer by sowmya(32)   (Show Source): You can put this solution on YOUR website!1.Derivatives: i)(Sin4x) /( x² +1) Let y = (sin4x)/x^2 +1 dy/dx use u/v method d(u/v) = (vdu-udv)/v^2 Here , u = sin4x v= x^2 +1 du = 4 cos4x dv = 2x dy/dx = ((x^2 +1)4cos4x- sin4x(2x))/(x^2 +1)^2 = (4x^2 cos4x + 4 cos4x - 2x sin4x)/(x^2+1)^2 ii)10t^2 +1 y = 10 t^2 +1 dy/dt = 20 t iii)y= sqrt((1+u)/(1-u)) y^2 = (1+u)/1-u) 2y dy = ((1-u) du + (1+u) du)/(1-u)^2 2y dy = 2du/(1-u)^2 y dy = du/(1-u)^2 dy/du = y/(1-u)^2 = sqrt((1-u)(1+u))/(1-u)^2 = (sqrt(1+u))/(1+u)^3/2 iv)question not clear