Derivative & Integral Rules

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d/dx(sinu)

(cosu)u’

d/dx(cosu)

-(sinu)u’

d/dx(tanu)

(sec^²u)u’

d/dx(cscu)

-(cscu cotu)u’

d/dx(secu)

(secu tanu)u’

d/dx(cotu)

-(csc²u)u’

d/dx(arcsinu)

u’/√(1-u²)

d/dx(arccosu)

-u’/√(1-u²)

d/dx(arctanu)

u’/(1+u²)

d/dx(arccscu)

-u’/abs(u)√(u²-1)

d/dx(arcsecu)

u’/absu √(u²-1)

d/dx(arccotu)

-u’/(1+u²)

d/dx(loga(u))

u’/(lna)u

d/dx(a^u)

(lna)a^u u’

int sinu du

-cosu + c

int cosu du

sinu + c

int tanu du

-ln abs(cosu) + c

int cscu du

-ln abs(cscu + cotu) + c

int secu du

ln abs(secu + tanu) + c

int cotu du

ln abs(sinu) + c

int du/√(a²-u²)

arcsin(u/a) + c

int du/(u²+a²)

(1/a)arctan(u/a) + c

int du/u√(u²-a²)

(1/a)arcsec(absu/a) + c

int a^u du

(1/lna)a^u + c