Variables

f, u, v
Functions
n
Integer
1.
Leibnitz's formula
(uv)=uv+2uv+uv\left(uv\right)^{\prime\prime}=u^{\prime\prime} v + 2u^\prime v^\prime + u v^{\prime\prime}
2.
Third derivative of a product
(uv)=uv+3uv+3uv+3uv\left(uv\right)^{\prime\prime\prime} = u^{\prime\prime\prime}v + 3u^{\prime\prime}v^\prime + 3u^\prime v^{\prime\prime} + 3uv^{\prime\prime\prime}
3.
n-th derivativative of xmx^m
(xm)(n)=m!(mn)!xmn\left(x^m\right)^{(n)}=\dfrac{m!}{(m-n)!}x^{m-n}
4.
n-th derivative of xnx^n
(xn)(n)=n!\left(x^n\right)^{(n)}=n!
5.
n-th derivative of logarithm
(logax)(n)=(1)n1(n1)!xnlnx\left( \log_a x\right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)! }{x^n \ln x}
6.
n-th derivative of natural logarithm
(lnx)(n)=(1)n1(n1)!xn\left(\ln x \right)^{(n)}=\dfrac{(-1)^{n-1} (n-1)!}{x^n}
7.
n th derivative od axa^x
(ax)(n)=axlnna\left(a^x\right)^{(n)}=a^x \ln^n a
8.
n-th derivative of exe^x
(ex)(n)=ex\left(e^x\right)^{(n)}=e^x
9.
(amx)(n)=mnaxlnna\left( a^{mx} \right)^{(n)} = m^n a^x \ln^na
10.
n-th derivativ of sin x
(sinx)(n)=sin(x+nπ2)\left( \sin x \right)^{(n)} = \sin\left(x+\dfrac{n\pi}{2}\right)
11.
n-th derivative od cos x
(cosx)(n)=cos(x+nπ2)\left( \cos x \right)^{(n)} = \cos\left(x+\dfrac{n\pi}{2}\right)