Diketahui f(x)=(1+sin x)/cos x maka f'(1/6pi)=....

f'(1/6pi) = 2

Pembahasan

Untuk mencari turunan f(x) = (1 + sin x) / cos x, kita gunakan aturan kuosien.
Misalkan u = 1 + sin x, maka u' = cos x.
Misalkan v = cos x, maka v' = -sin x.

f'(x) = (u'v - uv') / v^2
f'(x) = (cos x * cos x - (1 + sin x) * (-sin x)) / (cos x)^2
f'(x) = (cos^2 x + sin x + sin^2 x) / cos^2 x
f'(x) = (1 + sin x) / cos^2 x

Sekarang kita substitusikan x = \pi/6:
f'(pi/6) = (1 + sin(pi/6)) / cos^2(pi/6)
sin(pi/6) = 1/2
cos(pi/6) = sqrt(3)/2
cos^2(pi/6) = (sqrt(3)/2)^2 = 3/4

f'(pi/6) = (1 + 1/2) / (3/4)
f'(pi/6) = (3/2) / (3/4)
f'(pi/6) = (3/2) * (4/3)
f'(pi/6) = 2