삼각함수_미분표

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#noindex
Differentiation Formulas
http://archives.math.utk.edu/visual.calculus/2/formulas.1/index.html

||$f(x)$ ||$\frac{d}{dx}f(x)$ ||증명 ||
||$\sin x$ ||$\cos x$ ||[[RR:sin_x_미분_증명]] ||
||$\cos x$ ||$-\sin x$ ||[[RR:cos_x_미분_증명]] ||
||$\tan x$ ||$\sec^2 x$ ||[[RR:tan_x_미분_증명]] ||
||$\cot x$ ||$-\csc^2 x$ ||[[RR:cot_x_미분_증명]] 작성예정||
||$\sec x$ ||$\sec x \tan x$ ||
치역도 추가.
||$f(x)$ ||$\frac{d}{dx}f(x)$ ||정의역 ||증명 ||
||$\sin x$ ||$\cos x$ || ||[[RR:sin_x_미분_증명]] ||
||$\cos x$ ||$-\sin x$ || ||[[RR:cos_x_미분_증명]] ||
||$\tan x$ ||$\sec^2 x$ || ||[[RR:tan_x_미분_증명]] ||
||$\cot x$ ||$-\csc^2 x$ || ||[[RR:cot_x_미분_증명]] 작성예정||
||$\sec x$ ||$\sec x \tan x$ || ||[[RR:sec_x_미분_증명]] ||
||$\csc x$ ||$-\csc x \cot x$ ||
||$\sin^{-1}x$ ||$\frac{1}{\sqrt{1-x^2}}$ ||[[RR:arcsin_x(아크사인)_미분_증명]] ||
||$\cos^{-1}x$ ||$\frac{-1}{\sqrt{1-x^2}}$ ||[[RR:arccos_x(아크코사인)_미분_증명]] ||
||$\tan^{-1}x$ ||$\frac{1}{1+x^2}$ ||[[RR:arctan_x(아크탄젠트)_미분_증명]] ||
||$\sin^{-1}x$ ||$\frac{1}{\sqrt{1-x^2}}$ || ||[[RR:arcsin_x(아크사인)_미분_증명]] ||
||$\cos^{-1}x$ ||$\frac{-1}{\sqrt{1-x^2}}$ || ||[[RR:arccos_x(아크코사인)_미분_증명]] ||
||$\tan^{-1}x$ ||$\frac{1}{1+x^2}$ || ||[[RR:arctan_x(아크탄젠트)_미분_증명]] ||
||$\cot^{-1}x$ ||$\frac{-1}{1+x^2}$ ||
||$\sec^{-1}x$ ||$\frac{1}{|x|\sqrt{x^2-1}}$ ||[[RR:arcsec_x(아크시컨트)_미분_증명]] ||
||$\sec^{-1}x$ ||$\frac{1}{|x|\sqrt{x^2-1}}$ || ||[[RR:arcsec_x(아크시컨트)_미분_증명]] ||
||$\csc^{-1}x$ ||$\frac{-1}{|x|\sqrt{x^2-1}}$ ||
||$\sinh x$ ||$\cosh x$ ||
||$\cosh x$ ||$\sinh x$ ||
||$\tanh x$ ||$\operatorname{sech}^2 x$ ||
||$\tanh x$ ||$\operatorname{sech}^2 x$ || ||[[RR:tanh_x_미분_증명]] ||
||$\coth x$ ||$-\operatorname{csch}^2 x$ ||
||$\operatorname{sech} x$ ||$-\operatorname{sech} x \tanh x$ ||
||$\operatorname{csch} x$ ||$-\operatorname{csch} x \coth x$ ||
||$\sinh^{-1} x$ ||
||$\cosh^{-1} x$ ||
||$\tanh^{-1} x$ ||
||$\coth^{-1} x$ ||
||$\operatorname{sech}^{-1} x$ ||
||$\operatorname{csch}^{-1} x$ ||
||$\sinh^{-1} x$ ||$\frac1{\sqrt{x^2+1}}$ ||$\mathbb{R}$ ||이하 여섯개 CHK - 식은ok,정의역 chk||
||$\cosh^{-1} x$ ||$\frac1{\sqrt{x^2-1}}$ ||$x>1$ ||
||$\tanh^{-1} x$ ||$\frac1{1-x^2}$ ||$|x|<1$ ||
||$\coth^{-1} x$ ||$\frac1{1-x^2}$ ||$|x|>1$ ||
||$\operatorname{sech}^{-1} x$ ||$\frac{-1}{x\sqrt{1-x^2}}$ ||$0<x<1$ ||
||$\operatorname{csch}^{-1} x$ ||$\frac{-1}{|x|\sqrt{1+x^2}}$ ||$x\ne0$ ||
KWs:
derivatives of trigonometric functions
derivatives of inverse trigonometric functions
Derivatives of Hyperbolic Functions
Derivatives of Inverse Hyperbolic Functions
삼각함수 도함수/미분
삼각함수 역함수 도함수/미분
쌍곡선함수/쌍곡함수 도함수/미분
쌍곡선함수/쌍곡함수 역함수 도함수/미분
See also [[RR:여러가지증명]], [[RR:삼각함수적분표,trigonometric_integrals]]
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Up: [[미적분,calculus]], [[삼각함수,trigonometric_function]], [[쌍곡선함수,hyperbolic_function]], [[여러가지미분표와적분표]]



치역도 추가.
$f(x)$ $\frac{d}{dx}f(x)$ 정의역 증명
$\sin x$ $\cos x$ RR:sin_x_미분_증명
$\cos x$ $-\sin x$ RR:cos_x_미분_증명
$\tan x$ $\sec^2 x$ RR:tan_x_미분_증명
$\cot x$ $-\csc^2 x$ RR:cot_x_미분_증명 작성예정
$\sec x$ $\sec x \tan x$ RR:sec_x_미분_증명
$\csc x$ $-\csc x \cot x$
$\sin^{-1}x$ $\frac{1}{\sqrt{1-x^2}}$ RR:arcsin_x(아크사인)_미분_증명
$\cos^{-1}x$ $\frac{-1}{\sqrt{1-x^2}}$ RR:arccos_x(아크코사인)_미분_증명
$\tan^{-1}x$ $\frac{1}{1+x^2}$ RR:arctan_x(아크탄젠트)_미분_증명
$\cot^{-1}x$ $\frac{-1}{1+x^2}$
$\sec^{-1}x$ $\frac{1}{|x|\sqrt{x^2-1}}$ RR:arcsec_x(아크시컨트)_미분_증명
$\csc^{-1}x$ $\frac{-1}{|x|\sqrt{x^2-1}}$
$\sinh x$ $\cosh x$
$\cosh x$ $\sinh x$
$\tanh x$ $\operatorname{sech}^2 x$ RR:tanh_x_미분_증명
$\coth x$ $-\operatorname{csch}^2 x$
$\operatorname{sech} x$ $-\operatorname{sech} x \tanh x$
$\operatorname{csch} x$ $-\operatorname{csch} x \coth x$
$\sinh^{-1} x$ $\frac1{\sqrt{x^2+1}}$ $\mathbb{R}$ 이하 여섯개 CHK - 식은ok,정의역 chk
$\cosh^{-1} x$ $\frac1{\sqrt{x^2-1}}$ $x>1$
$\tanh^{-1} x$ $\frac1{1-x^2}$ $|x|<1$
$\coth^{-1} x$ $\frac1{1-x^2}$ $|x|>1$
$\operatorname{sech}^{-1} x$ $\frac{-1}{x\sqrt{1-x^2}}$ $0<x<1$
$\operatorname{csch}^{-1} x$ $\frac{-1}{|x|\sqrt{1+x^2}}$ $x\ne0$

KWs:
derivatives of trigonometric functions
derivatives of inverse trigonometric functions
Derivatives of Hyperbolic Functions
Derivatives of Inverse Hyperbolic Functions
삼각함수 도함수/미분
삼각함수 역함수 도함수/미분
쌍곡선함수/쌍곡함수 도함수/미분
쌍곡선함수/쌍곡함수 역함수 도함수/미분

See also RR:여러가지증명, RR:삼각함수적분표,trigonometric_integrals