Definition of Derivatives: | |
is the
derivative of

. The process of taking derivatives is called
differentiation.
Similarly, the
higher derivatives of

can be defined by
When there is more than one variable in a function, the derivative of the function should be specified
with respect to a particular variable. For example,
is the
partial derivative of
with respect to 
while keeping

and

constant.
In contrast to the
partial derivative, the
differential of

is defined by
Leibniz's Formula for Derivatives:
L'Hôspital's Rule: L'Hôspital's Rule is used to determine the indeterminates such as . If both and are differentiable in the domain except possibly at , then | |
The process can be repeated until the equivalent limit is found.
Integration by Parts: Integration by parts is one of the most commonly used integration formulas.
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