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Pembezaan fungsi trigonometri Terbitan fungsi-fungsi trigonometriFungsi | Terbitan pembezaan |
---|---|
sin ( x ) {\displaystyle \sin(x)} | d d x sin ( x ) = kos ( x ) {\displaystyle {d \over dx}\sin(x)=\operatorname {kos} (x)} |
kos ( x ) {\displaystyle \operatorname {kos} (x)} | d d x kos ( x ) = − sin ( x ) {\displaystyle {d \over dx}\operatorname {kos} (x)=-\sin(x)} |
tan ( x ) {\displaystyle \tan(x)} | d d x tan ( x ) = d d x ( sin ( x ) kos ( x ) ) = kos 2 ( x ) + sin 2 ( x ) kos 2 ( x ) = 1 + tan 2 ( x ) = sek 2 ( x ) {\displaystyle {d \over dx}\tan(x)={d \over dx}{\biggl (}{\sin(x) \over \operatorname {kos} (x)}{\biggr )}={\operatorname {kos} ^{2}(x)+\sin ^{2}(x) \over \operatorname {kos} ^{2}(x)}=1+\tan ^{2}(x)=\operatorname {sek} ^{2}(x)} |
sek ( x ) {\displaystyle \operatorname {sek} (x)} | d d x sek ( x ) = d d x ( 1 kos ( x ) ) = sin ( x ) kos 2 ( x ) = sek ( x ) tan ( x ) {\displaystyle {d \over dx}\operatorname {sek} (x)={d \over dx}{\biggl (}{1 \over \operatorname {kos} (x)}{\biggr )}={\sin(x) \over \operatorname {kos} ^{2}(x)}=\operatorname {sek} (x)\tan(x)} |
kosek ( x ) {\displaystyle \operatorname {kosek} (x)} | d d x kosek ( x ) = d d x ( 1 sin ( x ) ) = − kos ( x ) sin 2 ( x ) = − kotan ( x ) kosek ( x ) {\displaystyle {d \over dx}\operatorname {kosek} (x)={d \over dx}{\biggl (}{1 \over \sin(x)}{\biggr )}=-{\operatorname {kos} (x) \over \sin ^{2}(x)}=-\operatorname {kotan} (x)\operatorname {kosek} (x)} |
kotan ( x ) {\displaystyle \operatorname {kotan} (x)} | d d x kotan ( x ) = d d x ( kos ( x ) sin ( x ) ) = − kos ( x ) − sin 2 sin 2 ( x ) = − ( 1 + kot 2 ( x ) ) = − kosek 2 ( x ) {\displaystyle {d \over dx}\operatorname {kotan} (x)={d \over dx}{\biggl (}{\operatorname {kos} (x) \over \sin(x)}{\biggr )}={-\operatorname {kos} (x)-\sin ^{2} \over \sin ^{2}(x)}=-(1+\operatorname {kot} ^{2}(x))=-\operatorname {kosek} ^{2}(x)} |
Fungsi | Terbitan |
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arcsin ( x ) {\displaystyle \arcsin(x)} | 1 1 − x 2 {\displaystyle 1 \over {\sqrt {1-x^{2}}}} |
arccos ( x c ) {\displaystyle \operatorname {arccos} (xc)} | − 1 1 − x 2 {\displaystyle -1 \over {\sqrt {1-x^{2}}}} |
arctan ( x ) {\displaystyle \arctan(x)} | 1 1 + x 2 {\displaystyle 1 \over 1+x^{2}} |
arcsec ( x ) {\displaystyle \operatorname {arcsec}(x)} | 1 | x | 1 − x 2 {\displaystyle 1 \over |x|{\sqrt {1-x^{2}}}} |
arccsc ( x ) {\displaystyle \operatorname {arccsc}(x)} | − 1 | x | 1 − x 2 {\displaystyle -1 \over |x|{\sqrt {1-x^{2}}}} |
arccot ( x ) {\displaystyle \operatorname {arccot} (x)} | − 1 1 + x 2 {\displaystyle -1 \over 1+x^{2}} |
Rencana berkaitan matematik ini rencana tunas. Anda boleh membantu Wikipedia dengan mengembangkannya. |
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