What is the derivative of [tan x]
Sec^2x
The derivative of [tan x], where [ ] denotes the greatest integer function, does not exist for x = nπ + π/2, where n is an integer.
To understand this, we need to consider the greatest integer function. The greatest integer function returns the largest integer less than or equal to the real number. Thus, [tan x] will be a constant function over intervals of π radians where tan x is increasing and decreasing. In these intervals, the derivative of [tan x] will be zero.
However, at x = nπ + π/2, where n is an integer, the tangent function is undefined, and hence [tan x] is also undefined. As a result, the derivative of [tan x] not defined at these points.
In summary, the derivative of [tan x] exists and is equal to zero over intervals of π radians where tan x is increasing and decreasing, but it is not defined at points where x = nπ + π/2, where n is an integer.
More Answers:
Why The Composition Of Functions Is Not Commutative: Non-Commutativity In Mathematics.Composing Functions: Ensuring Domain Compatibility For Meaningful Outputs
How To Find The Derivative Of Cot X: Step-By-Step Guide With Quotient Rule