Jika f(x) = sin x cos x – sec x, nilai f'(π/4) =
Jika f(x) = sin x cos x – sec x, nilai f'(π/4) = ….
A. -1 - √2
B. -√2
C. 1 - √2
D. √2
E. 1 + √2
Pembahasan:
f(x) = sin x cos x – sec x
f'(x) = cos x cos x + sin x (-sin x) – sec x tan x
= cos2 x – sin2 x – sec x tan x
f'(π/4) = cos2 (π/4) – sin2 (π/4) – sec (π/4) tan (π/4)
= (½√2)2 – (½√2)2 – (√2) . 1
= ½ – ½ – √2
f'(π/4) = -√2
Jawaban: B
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