Turunan dari Invers Fungsi Trigonometri


\frac{d}{dx} arc sin x = …

y = arc sin x \Rightarrow sin y = x

\frac{d}{dx} sin y = \frac{d}{dx} x

cos y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{cos \quad y}

= \frac{1}{\sqrt{1-sin^2y}}

= \frac{1}{\sqrt{1-x^2}}

\frac{d}{dx} arc sin x = \frac{1}{\sqrt{1-x^2}}

.

\frac{d}{dx} arc cos x = …

y = arc cos x \Rightarrow cos y = x

\frac{d}{dx} cos y = \frac{d}{dx} x

-sin y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{-sin \quad y}

= \frac{-1}{\sqrt{1-cos^2y}}

= \frac{-1}{\sqrt{1-x^2}}

\frac{d}{dx} arc cos x = \frac{-1}{\sqrt{1-x^2}}

.

\frac{d}{dx} arc tan x = …

y = arc tan x \Rightarrow tan y = x

\frac{d}{dx} tan y = \frac{d}{dx} x

sec2 y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{sec^2 y}

= \frac{1}{1+tan^2y}

= \frac{1}{1+x^2}

\frac{d}{dx} arc tan x = \frac{1}{1+x^2}

.

\frac{d}{dx} arc csc x = …

y = arc csc x \Rightarrow csc y = x

\frac{d}{dx} csc y = \frac{d}{dx} x

-csc y cot y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{-csc(y).cot(y)}

= \frac{-1}{csc(y)\sqrt{csc^2y-1}}

= \frac{-1}{x\sqrt{x^2-1}}

\frac{d}{dx} arc csc x = \frac{-1}{x\sqrt{x^2-1}}

.

\frac{d}{dx} arc sec x = …

y = arc sec x \Rightarrow sec y = x

\frac{d}{dx} sec y = \frac{d}{dx} x

sec y tan y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{sec(y).tan(y)}

= \frac{1}{sec(y)\sqrt{sec^2y-1}}

= \frac{1}{x\sqrt{x^2-1}}

\frac{d}{dx} arc sec x = \frac{1}{x\sqrt{x^2-1}}

.

\frac{d}{dx} arc cotan x = …

y = arc cot x \Rightarrow cot y = x

\frac{d}{dx} cot y = \frac{d}{dx} x

-csc2 y \frac{dy}{dx} = 1

\frac{dy}{dx} = \frac{1}{-csc^2y}

= \frac{-1}{1+cot^2y}

= \frac{-1}{1+x^2}

\frac{d}{dx} arc cotan x = \frac{-1}{1+x^2}

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7 comments on “Turunan dari Invers Fungsi Trigonometri

  1. Ping-balik: Integral dari Invers Fungsi Trigonometri | Math IS Beautiful

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