Basic Differentiation Rules for Elementary Functions

Flashcards covering basic differentiation rules for elementary functions.

d/dx [c]

0

d/dx [x]

1

d/dx [u^n]

u’nu^(n-1)

d/dx [sin u]

u’cos(u)

d/dx [cos u]

-u’sin(u)

d/dx [tan u]

u'sec^2(u)

d/dx [cot u]

-u’csc^2(u)

d/dx [sec u]

u’(sec u tan u)

d/dx [csc u]

-u’(csc u cot u)

d/dx [ln u]

u'/u

d/dx [log_a u]

u'/(uln(a))

d/dx [a^u]

u’a^u(ln a)

d/dx [arcsin u]

u' / sqrt(1 - u^2)

d/dx [arccos u]

-u' / sqrt(1 - u^2)

d/dx [arctan u]

u' / (1 + u^2)

d/dx [arcsec u]

u' / (|u|sqrt(u^2 - 1))

d/dx [arccsc u]

-u' / (|u|sqrt(u^2 - 1))

d/dx [u/v]

(vu'-uv')/v^2

d/dx [uv]

uv'+vu'

d/dx [arccot(u)]

-u’/(1+u²)