Question

Kerjakan turunan fungsi trigonometri dari ..

Answer 1

Verified answer

Turunan

y = cos² (2x + π/4)

u = cos (2x + π/4)

du/dx = - 2 sin ( 2x + π/4)

y = u²

dy/du = 2u

*

dy/dx = dy/du. du/dx

= 2u. - 2 sin ( 2x + π/4)

= 2 cos (2x + π/4)  .  -2  sin (2x + π/4)

= -  2 { 2 sin (2x + π/4) cos (2x + π/4) }

= - 2  sin 2(2x + π/4)

= - 2 sin (4x + π/2)

*

x = π/4

*

dy/dx =   - 2  sin ( 4 . π/4  + π/4)

= - 2 sin ( π + π/4)

= - 2 sin (5π/4)

= - 2 sin (225°)

= - 2 sin (180 + 45)

= - 2 ( - sin 45)

= 2 sin 45

= 2 (1/2 √2)

= √2