1. Arcsin, Arccos, Arctan Paul Nettleton

2. Derivatives of Inverse trigonometric functions

3. 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”

4. 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

5. 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

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

7. Try Some Problems! d dx arcsin x² = d dx x² arcsin x = d dx = Click to view Answers Source: http://www.themathpage.com/acalc/inverse -trig.htm#arcsin http://www.themathpage.com/acalc/inverse -trig.htm#arcsin

8. Harder Problems d dx 3 arccos(x 2 + 0.5) 4 arctan3x 4 d dx Click to view Answers Source: http://www.intmath.com/Differentiation- transcendental/3_Derivative-arcsin-arccos- arctan.php http://www.intmath.com/Differentiation- transcendental/3_Derivative-arcsin-arccos- arctan.php