Equations Of Calculus

Limits:

the sum law

the product law

limit_x→af(g(x)) = f(limit_x→ag(x))

the root law and the power law

limit_x→0 [sin(x)/x] = 1

limit_x→0 [(cos(x)-1)/x] = 0

Differential Calculus:

the power rule (when exponent is a postive integer)

the product rule

the quotient rule

the chain rule

Using Euler's Number:

definition of e

[d/dx]b^x = b^xln(b)

[d/dx]log_bx = 1/(x * ln(b))

the power rule (when exponent is any real number)

only functions of the form Ae^x are derivatives of themselves

representing e^x as a limit

representing e^x as an infinite series (proof 1)

representing e^x as an infinite series (proof 2)

Euler's formula

Trigonometric Derivatives:

[d/dx]sin(x) = cos(x)

[d/dx]cos(x) = -sin(x)

derivative of sec(x) and cosec(x)

derivative of tan(x) and cotan(x)

derivative of arcsine(x)

derivative of arccosine(x)

derivative of arcsecant(x)

derivative of arccosecant(x)

derivative of arctangent(x)

derivative of arccotangent(x)

L'Hospital's Rule:

indeterminate form of type 0/0

Antiderivative:

antiderivative of 1/x (incomplete)

antiderivative of tangent(x) and cotangent(x)

antiderivative of secant(x) and cosecant(x)

Integral Calculus:

trapezium rule

fundamental theorem of calculus, part 1

fundamental theorem of calculus, part 2

integration by parts (incomplete)

using integration to find volume (incomplete)

using integration to find arc length (incomplete)

using integration to find surface area (incomplete)