Derivatives
At its core, a derivative measures how a function’s output value changes as its input value changes. In simpler terms, it calculates the slope of the tangent line to the curve of a function at any given point. Mathematically, the derivative of a function f(x)f(x)f(x) at a point xxx is defined as:
Basic Derivatives
Constant Rule
Examples:
Power Rule
Examples:
Sum and Difference Rule
Example:
Product Rule
Example:
Quotient Rule
Example:
Exponential Functions
Example:
Example:
Example:
Example:
Chain Rule
This theorem is called chain rule because it deals with a “chain” of functions.
Example:
Inserting the values:
Example:
remember the power rule? we must also take into consideration the power in a chain rule. Therefore, there is a constant 4 in the derivative and n-1=3 in the power.
