Definition of a Derivative
f'=limh->0 f(x+h)-f(x)/ h
d/dx(k)=
0
d/dx(k(u(x))=
k du/dx
d/dx(u^n)=
nu^n-1 du/dx
d/dx(u+v)=
du/dx+dv/dx
d/dx(u-v)=
du/dx-dv/dx
d/dx(uv)=
uv'+vu'
d/dx(u/v)=
vu'-uv'/v^2
d/dx(f(g(x))=
f'(g(x))g'(x)
dy/dx=
dy/du du/dx
d/dx(sinu)=
cosu du/dx
d/dx(cosu)=
-sinu du/dx
d/dx(tanu)=
sec^2u du/dx
d/dx(cotu)=
-csc^2u du/dx
d/dx(secu)=
secutanu du/dx
d/dx(cscu)=
-cscucotu du/dx
d/dx(sin^-1u)=
1/√1-u^2 du/dx
d/dx(cos^-1u)=
-1/√1-u^2 du/dx
d/dx(tan^-1u)=
1/u^2+1 du/dx
d/dx(cot^-1u)=
-1/u^2+1 du/dx
d/dx(sec^-1u)=
1/|u|√u^2-1 du/dx
d/dx(csc^-1u)=
-1/|u|√u^2-1 du/dx
d/dx(lnu)=
1/u du/dx
d/dx(logau)=
1/ulna du/dx
d/dx(e^u)=
e^u du/dx
d/dx(a^u)=
a^u lna du/dx
inverse d/dx g'(x)=
1/f'(g(x))