Fundamental quantities are the basic quantities that are used to describe the physical world. They are independent of each other and cannot be further broken down into simpler quantities. The seven fundamental quantities in the International System of Units (SI) are:

* Length (meter)

* Mass (kilogram)

* Time (second)

* Electric current (ampere)

* Thermodynamic temperature (kelvin)

* Amount of substance (mole)

* Luminous intensity (candela)

Derived Quantities:

Derived quantities are quantities that are expressed in terms of the fundamental quantities. They are obtained by combining the fundamental quantities using mathematical operations such as addition, subtraction, multiplication, and division. For example, the derived quantity of speed is defined as the distance traveled per unit time. The SI unit of speed is meters per second (m/s).

Here are some examples of derived quantities and their SI units:

* Area (square meter, m²)

* Volume (cubic meter, m³)

* Density (kilograms per cubic meter, kg/m³)

* Velocity (meters per second, m/s)

* Acceleration (meters per second squared, m/s²)

* Force (newtons, N)

* Pressure (pascals, Pa)

* Energy (joules, J)

* Power (watts, W)

The relationship between fundamental and derived quantities can be represented using dimensional analysis. Dimensional analysis involves identifying the units of the fundamental quantities that are involved in a derived quantity and expressing the derived quantity in terms of these units. For example, the SI unit of speed (m/s) is obtained by dividing the SI unit of distance (meter) by the SI unit of time (second).

Dimensional analysis is a useful tool for checking the validity of equations and for converting units from one system to another.