Carilah derivatif dari fungsi y = ln (cos(e2x - 2x))

jawab

turunan y = ln ( cos (e²ˣ - 2x))
substitusi
u =e²ˣ - 2x
du/dx = 2 e²ˣ - 2 = 2 (e²ˣ -1)

v = cos u
dv/du = - sin u

y = ln v
dy/dv = 1/v

dy/dx =  dy/dv . dv/du. du.dx
dy/dx = 1/v .(-sin u) (2)(e²ˣ -1)
dy/dx = (1/cos u)(- sin u) (2) (e²ˣ - 1)
dy/dx = - 2 (sin u)/(cos u)(e²ˣ - 1)
dy/dx = - 2 (e²ˣ - 1) tan u
dy/dx = - 2(e²ˣ -1) tan (e²ˣ - 2x)