Calculus Differentiation and Integration Rules

derivative of x^n

nx^n-1

derivative of sin(x)?

cos(x).

derivative of cos(x)?

-sin(x).

derivative of tan(x)?

sec²(x).

derivative of cot(x)?

-csc²(x).

derivative of sec(x)?

sec(x)tan(x)

derivative of csc(x)?

-csc(x)cot(x)

derivative of ln(u)

u'/u

derivative of e^u?

e^u u'

integral of sin(u)?

-cos(u) + C.

integral of cos(u)?

sin(u) + C.

integral of tan(u)

-ln |cos(u)| + C

integral of cot(u)

ln|sin(u)| + C

integral of sec(u)

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

integral of csc(u)

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

integral of sec²(u)?

tan(u) + C.

integral of csc²(u)

-cot(u) + C

integral of sec(u)tan(u)

sec(u) + C

integral of csc(u)cot(u)

-csc(u) + C

integral of du

u + C

integral of u^n

u^(n+1)/(n+1) +C

integral of du/u

ln |u| + C

integral of e^u

e^u + C

Integral of a^u

a^u/ln(a) + C

Integral of du/square root 1- u^2

arcsin(u) + C

Integral of du/1 + u^2

arctan(u) + C

Integral of du/u * square root u^2 - 1

arcsec(u) + C

Volume of Cross Section for Squares

A = S^2

Volume of Cross Section of Equilateral Triangle

A = square root 3/4 * S^2

Volume of Cross Section of Isosceles Right Triangle

A = S^2/2 or S^2/4

Volume of Cross Section of Rectangles

A = Sh

Volume of Cross Section of Semi-Circle

piS^2/8