Terbitan fungsi-fungsi trigonometri Pembezaan fungsi trigonometri

Fungsi trigonometri asas

Terbitan pembezaan fungsi trigonometri asas
FungsiTerbitan 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 trigonometri songsang

Terbitan pembezaan fungsi trigonometri songsang
FungsiTerbitan
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.