Natural Logarithm

There is a unique positive number
e
such that the function
f (t) = e
^{t}
is its own derivative. The
natural logarithm of a positive real number
x
is the
logarithm of
x
with base
e
, denoted
log(x)
.
Alternately,
log(x) =


Chain Rule

The formula for the derivative of a composition of functions. If
h(x) = f
o
g(x) = f (g(x)
, then:
Implicit Differentiation

A method for differentiating implicit functions, without necessarily solving for them, by differentiating the terms of the defining equation.
Product Rule

The formula for the derivative of a product of functions:
[f (x)g(x)] = f (x)g'(x) + g(x)f'(x)


Quotient Rule

The formula for the derivative of a quotient of functions (which is a consequence of the product rule). If
q(x) = f (x)/g(x)
, then:
q'(x) =

