derivative memorization terms

d/dx[cu]

cu'

(d/dx) u+- v

u'+-v'

d/dx[uv]

uv'+vu'

d/dx [u/v]

(vu'-uv')/v^2

d/dx[c]

0

D/dx [u^n]

nu^(n-1)u'

d/dx[x]

=1

d/dx[|u|]

(u/|u|)u'

d/dx [ln u]

u'/u

d/dx e^u

e^u u'

d/dx loga(u)

u'/(lna)u

d/dx [a^u]

(lna)(a^u)(u')

d/dx sinu

(cosu)u'

d/dx cosu

-(sinu)u'

d/dx tanu

(sec^2u)u'

d/dx cscu

-(csc u cot u)u'

d/dx secu

(secutanu)u'

d/dx cotu

-(csc^2u)u'

d/dx arcsin u

u'/√(1-u^2)

d/dx arccos u

-u'/√(1-u^2)

d/dx arctan u

u'/(1+u^2)

d/dx arccsc u

-u'/(|u|√(u^2-1))

d/dx arcsec u

u'/(|u|√(u^2-1))

d/dx arccot u

-u'/(1+u^2)