Derivative List

Properties

Rule Name Derivative
\( \dfrac d{dx}[u \pm v] = u' \pm v' \)
\( \dfrac d{dx}[uv] = uv' + vu' \)
\( \dfrac d{dx}[\dfrac uv] = \dfrac {vu' - uv'}{v^2} \)

Basic

Rule Name Derivative
\( \dfrac d{dx}[cx] = c \)
\( \dfrac d{dx}[c] = 0 \)
\( \dfrac d{dx}[x^n] = nx^{n-1} \)
\( \dfrac d{dx}[e^x] = e^x \)
\( \dfrac d{dx}[a^x] = a^xln(a) \)
\( \dfrac d{dx}[log_ax] = \dfrac 1{xln(a)} \)
\( \dfrac d{dx}[ln(x)] = \dfrac 1x \)
\( \dfrac d{dx}[x] = 1 \)

Trig

Rule Name Derivative
\( \dfrac d{dx}[sin(ax)] = acos(ax) \)
\( \dfrac d{dx}[cos(x)] = -sin(x) \)
\( \dfrac d{dx}[tan(x)] = sec^2(x) \)
\( \dfrac d{dx}[sec(x)] = sec(x)tan(x) \)
\( \dfrac d{dx}[cot(x)] = -csc^2(x) \)
\( \dfrac d{dx}[csc(x)] = -csc(x)cot(x) \)

Inverse Trig

Rule Name Derivative
\( \dfrac d{dx}[arcsin(x)] = \dfrac 1{\sqrt{1-x^2}} \)
\( \dfrac d{dx}[arctan(x)] = \dfrac 1{1 + x^2} \)
\( \dfrac d{dx}[arcsec(x)] = \dfrac 1{|x|\sqrt{x^2 - 1}} \)
\( \dfrac d{dx}[arccos(x)] = \dfrac {-1}{\sqrt{1-x^2}} \)
\( \dfrac d{dx}[arccot(x)] = \dfrac {-1}{1 + x^2} \)
\( \dfrac d{dx}[arccsc(x)] = \dfrac {-1}{|x|\sqrt{x^2 - 1}} \)