Question 167547
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