The derivative
It could also be defined as limit expressions
Derivative can also be expressed as an instantaneous rate of change or estimated by average rate of change
Common derivatives
Constant, Exponential and Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Functions
High-order derivative
Any derivative beyond the first
Rules
Algebra of derivatives
- Multiply a function by a constant
- Add or subtract two functions
power rule
chain rule
product rule
Inverse function
If
For example, let
Application
Example 1: related rates
The radius of a sphere is decreasing at a rate of 1 meter per hour. At a certain instant
, the radius is 4 meters. What is the rate of change of the volume of the sphere at that instant (in cubic meters per hour)? We know:
Find: