Derivative Basic Rules

d/dx [cu]

cu'

d/dx [uv]

uv' + vu'

d/dx [u±v]

u' ± v'

d/dx [u/v]

(vu' - uv')/v²

d/dx [c]

0

d/dx [uⁿ]

nuⁿ⁻¹u'

d/dx [ln u]

u'/u

d/dx [eᵘ]

eᵘu'

d/dx [loga u]

u'/(ln a × u)

d/dx a^u

(ln a) a^u u'

d/dx [sin(u)]

u'[cos (u)]

d/dx [cos(u)]

-u'[sin (u)]

d/dx [tan(u)]

u'[sec²(u)]

d/dx [cot(u)]

-u'[csc²(u)]

d/dx [sec(u)]

u'[sec(u) tan(u)]

d/dx [csc(u)]

-u'[csc(u)cot(u)]

d/dx [sin⁻¹(u)]

u'/√(1-u²)

d/dx [cos⁻¹(u)]

-u'/√(1-u²)

d/dx [tan⁻¹(u)]

u'/(1+u²)

d/dx [cot⁻¹(u)]

-u'/(1+u²)

d/dx [sec⁻¹(u)]

u'/|u|√(u²-1)

d/dx [csc⁻¹(u)]

u'/|u|√(u²-1)