Appendix B
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APPENDIX B| TABLE OF DERIVATIVES General Formulas 1. d dx ( c ) =0 2. d dx ⎛ ⎝ f ( x )+ g ( x ) ⎞ ⎠ = f ′( x )+ g ′( x ) 3. d dx ⎛ ⎝ f ( x ) g ( x ) ⎞ ⎠ = f ′( x ) g ( x )+ f ( x ) g ′( x ) 4. d dx ( x n ) = nx n −1 , for real numbers n 5. d dx ⎛ ⎝ cf ( x ) ⎞ ⎠ = cf ′( x ) 6. d dx ⎛ ⎝ f ( x )− g ( x ) ⎞ ⎠ = f ′( x )− g ′( x ) 7. d dx ⎛ ⎝ f ( x ) g ( x ) ⎞ ⎠ = g ( x ) f ′( x )− f ( x ) g ′( x ) ⎛ ⎝ g ( x ) ⎞ ⎠ 2 8. d dx ⎡ ⎣ f ⎛ ⎝ g ( x ) ⎞ ⎠ ⎤ ⎦ = f ′ ⎛ ⎝ g ( x )
⎞ ⎠ · g ′( x ) Trigonometric Functions 9. d dx (sin x ) =cos x 10. d dx (tan x ) = sec 2 x 11. d dx (sec x ) = sec x tan x 12. d dx (cos x ) =−sin x 13. d dx (cot x ) =−csc 2 x 14. d dx (csc x ) =−csc x cot x Inverse Trigonometric Functions 15. d dx ⎛ ⎝ sin −1 x ⎞ ⎠ = 1 1− x 2 16. d dx ⎛ ⎝ tan −1 x ⎞ ⎠ = 1 1+ x 2 17. d dx ⎛ ⎝ sec −1 x ⎞ ⎠ = 1 | x | x 2 −1
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