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d/dx sin
cos
d/dx tan
sec^2
d/dx cot
-csc^2
d/dx csc
-cscxcotx
d/dx sec
secxtanx
d/dx cos
-sin
d/dxarcsinu
1/sqrt(1-u^2) *du/dx
d/dx arccosu
-1/sqrt(1-u^2) *du/dx
d/dx arctanu
1/1+u^2 *du/dx
d/dx arccotu
-1/(1+u^2) *du/dx
d/dx arccscu
-1/u(sqrt(u^2-1)) *du/dx
d/dx arcsecu
1/u(sqrt(u^2-1)) *du/dx
product rule
f(x)g'(x)+f'(x)g(x)
quotient rule
g(x)f'(x)-f(x)g'(x) / g(x)^2
sin^2(x)+cos^2(x)=
1
cos^2(x)-1=
-sin^2(x)
sin(a+b)=
sinacosb+cosasinb
f(u(x))=
(f'(u))(u'(x))
d/dx (e^u)=
d/du(e^u)(d/dx(u))
d/dx ln(f(x))=
f'(x)/f(x)
d/dx ln(g(u))=
g'(u)/g(u) *u'
d/dx ln(x)
1/x
d/dx log(base a)x=
1/xln(a)
d/dx log(base a)u=
1/uln(a) *u'
exponential equation
y(t)= Y(i)e^kt
areas of circle
Pi*r^2
Surface of a cylinder
2pirh+ 2pi*r^2
Volume of a prism
Bh
Area of a trapezoid
h(a+b) /2
Volume of a pyramid
1/3*bh
Surface of a sphere
4πr^2
Volume sphere
4/3πr³