Calc BC Derivatives Rules

A & C represent constants; U, V, & X represent variables

d/dx[cu] =

cu’

d/dx[u ± v] =

u’ ± v’

d/dx[u • v] =

uv’ + vu’ (product rule)

d/dx[u/v] =

(vu’ – uv’)/v² (quotient rule)

d/dx[c] =

0

d/dx[uⁿ] =

nu^n–1u’ (power rule)

d/dx[x] =

1

d/dx[|u|] =

u/|u| • u’ (u ≠ 0)

d/dx[lnu] =

u’/u

d/dx[e^u] =

e^uu’

d/dx[log_au] =

u’/((lna)u)

d/dx[a^u] =

(lna)a^uu’

d/dx[sinu] =

(cosu)u’

d/dx[cosu] =

–(sinu)u’

d/dx[tanu] =

(sec²u)u’

d/dx[cotu] =

–(csc²u)u’

d/dx[secu] =

(secu • tanu)u’

d/dx[cscu] =

–(cscu • cotu)u’

d/dx[arcsinu] =

u’/sqrt(1 – u²)

d/dx[arctanu] =

u'/(1 + u²)