Arcsin, Arccos, Arctan Paul Nettleton

Derivatives of Inverse trigonometric functions

Deriving Derivative of Arcsin sin²y + cos²y = 1 y = arcsinx sin y = x Pythagorean Idendity Find the Derivative by Implicit Differentiation cos y = 1 = Substitute Substitute “x” for “sin y”

Deriving Derivative of Arccos sin²y + cos²y = 1 y = arccosx cos y = x Pythagorean Idendity Find the Derivative by Implicit Differentiation -sin y = 1 Substitute “x” for “cos y” = _ sin y = Substitute

Deriving Derivative of Arctan y = arctan x tan y = x Find the Derivative by Implicit Differentiation sec ² y = 1 A = sec ² y 1 Substitute A = 1 + tan²y 1 Substitute “x” for “tan y” 1 + tan²y = sec²y Pythagorean Identity

Integrals of Inverse Trigonometric Functions According to the Fundamental Theorem of Calculus

Try Some Problems! d dx arcsin x² = d dx x² arcsin x = d dx = Click to view Answers Source: -trig.htm#arcsin -trig.htm#arcsin

Harder Problems d dx 3 arccos(x ) 4 arctan3x 4 d dx Click to view Answers Source: transcendental/3_Derivative-arcsin-arccos- arctan.php transcendental/3_Derivative-arcsin-arccos- arctan.php