
The
derivative of a power is the exponent times x to the power of the exponnent
minus one.


The
derivative of a sum is the sum of the derivatives of each function being
added.


The
derivative of a difference is the difference of the derivatives of the functions
being subtracted.


The
derivative of a constant times a function is the constant times the derivative
of the function.


The
derivative of a constant is zero.


The
derivative of a product is the derivative of the first factor multiplied
by the second factor plus the first factor multiplied by the derivative
of the second factor.


The
derivative of a quotient is the quotient of the derivative of the numerator
multiplied by the denominator minus the numerator multiplied by the derivative
of the denominator to the square of the denominator.


The
derivative of an exponential function is the product of the exponential
function and the natural logarithm of the base.


Since
the natural logarithm of e is 1, the derivative of e^(x) is e^(x).


The
derivative of a logarithm is 1 divided by the product of the natural logarithm
of the base and x.


The
derivative of the natural logarithm of x is 1/x.


The
derivative of the sine of x is the cosine of x.


The
derivative of the cosine of x is the opposite of the sine of x.


The
derivative of the tangent of x is the square of the secant of x.


The
derivative of the secant of x is the product of the secant of x and the
tangent of x.


The
derivative of the cosecant of x is the opposite of the product of the cosecant
of x and the cotangent of x.


The
derivative of the cotangent of x is the opposite of the square of the cosecant
of x.
