Lihat sumber bagi Pembezaan fungsi trigonometri

{{Trigonometry}}
'''Pembezaan fungsi trigonometri''' merangkumi proses-proses matematik [[pembezaan]] kepada suatu [[fungsi trigonometri]], yakni kadar perubahan berdasarkan suatu pemalar.

Semua hasil pembezaan bagi fungsi trigonometri boleh diterbitkan melalui proses pembezaan sin(x) dan kos(x). Peraturan hasil bahagi kemudiannya digunakan untuk menerbitkan hasil-hasil pembezaan lain.

== Terbitan fungsi-fungsi trigonometri ==

=== Fungsi trigonometri asas ===
{| class="wikitable"
|+Terbitan pembezaan fungsi trigonometri asas
!Fungsi
!Terbitan pembezaan
|-
|<math>\sin(x)</math>
|<math>{d \over dx}\sin(x) = \operatorname{kos}(x)</math>
|-
|<math>\operatorname{kos}(x)</math>
|<math>{d \over dx}\operatorname{kos}(x) = -\sin(x)</math>
|-
|<math>\tan(x)</math>
|<math>{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)</math>
|-
|<math>\operatorname{sek} (x)</math>
|<math>{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)</math>
|-
|<math>\operatorname{kosek} (x)</math>
|<math>{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)</math>
|-
|<math>\operatorname{kotan} (x)</math>
|<math>{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)</math>
|}

=== Fungsi trigonometri songsang ===
{| class="wikitable"
|+Terbitan pembezaan fungsi trigonometri songsang
!Fungsi
!Terbitan
|-
|<math>\arcsin(x)</math>
|<math>1 \over \sqrt{1 - x^2}</math>
|-
|<math>\operatorname{arccos}(xc)</math>
|<math>-1 \over \sqrt{1 - x^2}</math>
|-
|<math>\arctan(x)</math>
|<math>1 \over 1 + x^2</math>
|-
|<math>\arcsec(x)</math>
|<math>1 \over |x|\sqrt{1 - x^2}</math>
|-
|<math>\arccsc(x)</math>
|<math>-1 \over |x| \sqrt{1 - x^2}</math>
|-
|<math>\arccot(x)</math>
|<math>-1 \over 1 + x^2</math>
|}
{{Tunas-math}}
[[Kategori:Kalkulus pembezaan]]
[[Kategori:Persamaan pembezaan]]