Derivative of inverse trigonometric functions - Derivatives

Derivative of inverse trigonometric functions

In this section, we will study the differential rules of inverse trigonometric functions, also known as cyclometric functions and arc-functions. Using our knowledge of inverse relations, and the definitions of the trigonometric functions “SOH CAH TOA”, we will learn to derive the derivative formulas for inverse trig functions.


Trigonometric Identities – “Pythagorean Identities”
sin2θ+cos2θ=1{si}{{n}^2}\theta \; + {\;co}{{s}^2}\theta \; = \;1
1+tan2θ=sec2θ1{\;} + {\;ta}{{n}^2}\theta \; = \;{se}{{c}^2}\theta
1+cot2θ=csc2θ1{\;} + {\;co}{{t}^2}\theta \; = \;{cs}{{c}^2}\theta
Here are formulas to deriving inverse trigonometric functions
ddx(\frac{d}{dx}(arcsin x)=11x2 x)=\frac{1}{\sqrt{1-x^2}}
ddx(\frac{d}{dx}(arccos x)=11x2x)=\frac{-1}{\sqrt{1-x^2}}
ddx(\frac{d}{dx}(arctan x)=11+x2x)=\frac{1}{1+x^2}
ddx(\frac{d}{dx}(arccot x)=11+x2 x)=\frac{-1}{1+x^2}
ddx(\frac{d}{dx}(arcsec x)=1xx21 x)=\frac{1}{|x| \sqrt{x^2-1}}
ddx(\frac{d}{dx}(arccsc x)=1xx21 x)=\frac{-1}{|x| \sqrt{x^2-1}}
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Derivative of inverse trigonometric functions

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