Rule/Identity Memorization Flashcards
What is the derivative of u * v? (Product Rule)
uv’ + vu’
What is the derivative of u / v? (Quotient Rule)
vu’ - uv’ / v^2
What is the derivative of u^n? (Power Rule)
nu^(n-1)*u’
What is the derivative of |u|?
u / |u| * u’ where u != 0
What is the derivative of ln u?
u’ / u
What is the derivative of e^u?
e^u * u’
What is the derivative of log_a_u?
u’ / (ln a) * u
What is the derivative of a^u?
(ln a) * a^u * u’
What is the derivative of sin u?
cos u * u’
What is the derivative of cos u?
-(sin u) * u’
What is the derivative of tan u?
sec^2 u * u’
What is the derivative of cot u?
-(csc^2 u) * u’
What is the derivative of sec u?
(sec u tan u) * u’
What is the derivative of csc u?
-(csc u cot u) * u’
What is the derivative of arcsin u?
u’ / sqrt(1 - u^2)
What is the derivative of arccos u?
-u’ / sqrt(1 - u^2)
What is the derivative of arctan u?
u’ / 1 + u^2
What is the derivative of arccot u?
-u’ / 1 + u^2
What is the derivative of arcsec u?
u’ / |u| * sqrt(u^2 - 1)
What is the derivative of arccsc u?
-u’ / |u| * sqrt(u^2 -1)
What is the derivative of sinh u?
(cosh u) * u’
What is the derivative of cosh u?
(sinh u) * u’
What is the derivative of tanh u?
(sech^2 u) * u’
What is the derivative of coth u?
-(csch^2 u) * u’