THOMAS CALCULUS 14TH EDITION
REVIEW SHEET 2026 FULL
PROBLEMS AND CORRECT
SOLUTIONS
◉ d/dx arccos(u). Answer: −u'/√(1−u²)
◉ d/dx arctan(u). Answer: u'/(u²+1)
◉ d/dx arccot(u). Answer: −u'/(u²+1)
◉ d/dx arcsec(u). Answer: u'/(|u|√(u²-1))
◉ d/dx arccsc(u). Answer: −u'/(|u|√(u²-1))
◉ ∫u'/√(a²−u²)dx. Answer: arcsin(u/a)+C
◉ ∫u'/(u²+a²) dx. Answer: (1/a)arctan(u)+C
◉ ∫u'/(u√(u²-a²))dx. Answer: (1/a)arcsec(|u|/a)+C
◉ d/dx sin(u). Answer: cos(u)u'
REVIEW SHEET 2026 FULL
PROBLEMS AND CORRECT
SOLUTIONS
◉ d/dx arccos(u). Answer: −u'/√(1−u²)
◉ d/dx arctan(u). Answer: u'/(u²+1)
◉ d/dx arccot(u). Answer: −u'/(u²+1)
◉ d/dx arcsec(u). Answer: u'/(|u|√(u²-1))
◉ d/dx arccsc(u). Answer: −u'/(|u|√(u²-1))
◉ ∫u'/√(a²−u²)dx. Answer: arcsin(u/a)+C
◉ ∫u'/(u²+a²) dx. Answer: (1/a)arctan(u)+C
◉ ∫u'/(u√(u²-a²))dx. Answer: (1/a)arcsec(|u|/a)+C
◉ d/dx sin(u). Answer: cos(u)u'
