tentukan turunan fungsi y= tan (3x-1)

jawab

y = tan (3x - 1)

y = sin(3x - 1) /cos (3x -1)
y = u /v
y' =  U'v - uv')/(v)²

u= sin (3x -1) → u'= 3 cos (3x-1)
v= cos (3x-1) → v'= - 3 sin (3x-1)

y' = { (3 cos (3x-1)( cos (3x- 1) - { sin(3x-1)(-3 sin (3x -1)} /(cos² (3x-1))
y' = { 3 cos² (3x-1) + 3 sin² (3x -1)}/ (cos² (3x-1))
y' = 3  { cos² (3x-1) + sin² (3x-1) }/ (cos² (3x-1)
y' = 3 (1)/(cos²(3x-1)
y' = 3 sec² (3x -1)

Diferensial
>> TRIgonomeTRI

d/dx (tan x) = sec² x

y = tan (3x - 1)

y'
= dtan (3x - 1) /d(3x - 1) × d(3x - 1)/dx
= sec² (3x - 1) . 3
= 3 sec² (3x - 1)