calc formulas - basic derivatives, integrals, and double/half angle

d/dx sin⁻¹(u)

u’/sqrt(1-u^2)

d/dx cos⁻¹(u)

-u’/sqrt(1-u^2)

d/dx tan⁻¹(u)

u’/(1+u^2)

d/dx csc⁻¹(u)

-u’/(|u|sqrt((u^2)-1))

d/dx sec⁻¹(x)

u’/(|u|sqrt((u^2)-1))

d/dx cot⁻¹(x)

-u’/(1+u^2)

d/dx (e^u)

e^u * u’

d/dx (lnx)

1/x

d/dx (lnu)

u’/u

d/dx (a^u)

lna * a^u * u’

d/dx (log_au)

u’/u(ln(a))

inverse derivatives f’(x)

1/(f’(g(x))

d/dx |u|

(u * u’)/|u|

integral of sin(u)du

-cos(u) + c

integral of cos(u)du

sin(u) + c

integral of tan(u)du

-ln|cos(u)| + c

integral of cot(u)du

ln|sin(u)| + c

integral of sec(u)du

ln|sec(u) + tan(u)| + c

integral of csc(u)du

-ln|csc(u) + cot(u)| + c

integral of sec^2(u)du

tan(u) + c

integral of csc^2(u)du

-cot(u) + c

integral of sec(u)tan(u)du

sec(u) + c

integral of csc(u)cot(u)du

-csc(u)+c

integral of du/(sqrt(a^2-u^2)

arcsin(u/a) + c

integral of du/u*sqrt(u^2-a^2)

1/a*arcsec(|u|/a) + c

integral of du/(a^2+u^2)

1/a*arctan(u/a) + c

d/dx sin(u)

cos(u)u’

d/dx cos(u)

-sin(u)u’

d/dx tan(u)

sec^2(u)u’

d/dx cot(u)

-csc^2(u)u’

d/dx sec(u)

sec(u)tan(u)u’

d/dx csc(u)

-csc(u)cot(u)u’

sin(2u)

2sin(u)cos(u)

cos(2u)

cos^2(u)-sin^2(u) | 2cos^2(u) - 1 | 1 - 2sin^2(u)

tan(2u)

2tan(u)/(1-tan^2(u))

sin^2(u)

(1-cos(2u))/2

cos^2(u)

(1+cos(2u))/2

tan^2(u)

(1-cos(2u))/(1+cos(2u))