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Derivative of an Integral

Description

This equation is part of the fundamental theorem of calculus, and shows that the derivative of an integral, is the contents of the integral.

\[\frac{\htmlClass{sdt-0000000102}{\:d}}{\htmlClass{sdt-0000000102}{\:d} \htmlClass{sdt-0000000003}{x}} (\htmlClass{sdt-0000000060}{\int} \htmlClass{sdt-0000000096}{f}(\htmlClass{sdt-0000000003}{x}) \htmlClass{sdt-0000000102}{\:d} \htmlClass{sdt-0000000003}{x}) = \htmlClass{sdt-0000000096}{f}(\htmlClass{sdt-0000000003}{x})\]

Symbols Used:

This is a symbol for any generic variable. It can hold any value, whether that be an integer or a real number, or a complex number, or a matrix etc.

\( \int \)

This is the symbol for an integral, sometimes referred to as an antiderivative. Graphically, it can be understood as the area between a curve and the axis the integral is taken with respect to.

\( f \)

This is the symbol for a function. It is commonly used in algebra, and (multivariate) calculus.

\( \:d \)

This is the symbol for a differential. It represents an infinitesimally small (infinitely close to zero) change in whatever variable it is with respect to.

Derivation

Coming soon...

Example

Example coming soon...