Jika f(x) = sin^2 x / cos x , maka f' (phi/4) = Siapa bisa jawab?

f(x) = sin²x / cosx
misal u= sin²x maka u' = 2sinxcosx
dan
v= cosx maka v'=-sinx

sehingga
f'(x) = u'v - v'u / v²
= (2sinxcosx)(Cosx) - (-Sinx) (Sin²x) / (cos²x)
= 2Cos²x (sinx) + 1/cos²x(sin³x) / cos²x
= 2sinx +(sin³x / cos²x)

π/4= 180/4= 45°

maka
f'(45°)= 2sin45° + (sin³45° / cos²45°)
= 2(½√2) + ((½√2)³ / ½√2)²
= √2 + ½√2
=3/2 √2