Calculus- general topics

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.