Trigonometri og differentiation

3 cos ( x ) e-x + 3 sin ( x ) y = cos ( 3 x ) + 2 sin ( 2 x )

f (x) = 3 ⋅ cos(x) ⋅ e−x + 3 ⋅ sin(x) g (x) = f ' (x) = 3 (cos(x))' ⋅ e−x + 3 cos(x) ⋅ (e−x)' + 3 cos(x) = −3 sin(x) ⋅ e−x + 3 cos(x) ⋅ (−e−x) + 3 cos(x) = −e−x ⋅ 3 sin(x) − e−x ⋅ 3 cos(x) + 3 cos(x) = −e−x (3 sin(x) + 3 cos(x)) + 3 cos(x) f (x) = cos(3x) + 2 ⋅ sin(2x) g (x) = f ' (x) = (cos (3x))' + 2 ⋅ (sin (2x))' = −sin(3x) ⋅ (3x)' + 2 ⋅ cos(2x) ⋅ (2x)' = − sin(3x) ⋅ 3 + 2 ⋅ cos(2x) ⋅ 2