Carilah turunan fungsi trigonometri berikut
[tex]\displaystyle y=\frac{1}{1+\sin x}+\frac{1}{1+\cos x}+\frac{1}{1+\tan x}+\frac{1}{1+\cot x}+\frac{1}{1+\sec x}+\frac{1}{1+\csc x}[/tex]
[tex]\displaystyle y=\frac{1}{1+\sin x}+\frac{1}{1+\cos x}+\frac{1}{1+\tan x}+\frac{1}{1+\cot x}+\frac{1}{1+\sec x}+\frac{1}{1+\csc x}[/tex]
Verified answer
TURUNAN
y = c ⇢ y' = 0
1/(1 + sin a) + 1/(1 + csc a)
= 1/(1 + sin a) + sin a/(1 + sin a)
= (1 + sin a)/(1 + sin a)
= 1
1/(1 + cos a) + 1/(1 + sec a)
= 1/(1 + cos a) + cos a/(1 + cos a)
= (1 + cos a)/(1 + sin a)
= 1
1/(1 + tan a) + /(1 + cotan a ) = 1
•
[tex] \displaystyle \sf \: y=\frac{1}{1+\sin x}+\frac{1}{1+\cos x}+\frac{1}{1+\tan x}+\frac{1}{1+\cot x}+\frac{1}{1+\sec x}+\frac{1}{1+\csc x} \: = \: 3 \\ \\ \boxed{\displaystyle \sf \frac{dy}{dx} = 0}[/tex]
•
a/b ⇢ b ≠ 0
dg x memenuhi syarat penyebut