Aplikasi Turunan

Persamaan Garis Singgung

Turunan

f(x) = 3x sin 2x

misal :

u = 3x → u' = 3

v = sin 2x → v' = 2 cos 2x

f(x) = uv

turunan pertama → f'(x)

f'(x) = u'v + uv'

f'(x) = 3 sin 2x + 3x . 2 cos 2x

f'(x) = 3 sin 2x + 6x cos 2x

absis x = π/4

gradien m = f'(π/4)

= 3 sin 2(π/4) + 6(π/4) . cos 2(π/4)

= 3 sin (π/2) + 3π/2 . cos (π/2)

= 3 sin 90° + 3π/2 cos 90°

= 3 . 1 + 3π/2 . 0

= 3

y = f(π/4) = 3(π/4) sin (2 × π/4)

y = 3π/4 sin 90°

y = 3π/4

titik singgung (π/4 , 3π/4)

PGS dg gradien m di titik singgung (π/4 , 3π/4) :

y = m(x - x1) + y1

y = 3(x - π/4) + 3π/4

y = 3x