Derivative of tan x
How to find the derivative of the given function by using the derivative of tan x: formula, 1 example, and its solution.
Formula
The derivative of tan x, [tan x]',
is sec2 x.
(not cot x)
Exampley = x2 tan x, y' = ?
Solution
Solution (Detail)
x2 tan x
is the product of x2 and tan x.
So the derivative of the product is,
the derivative of x2, 2x1
times tan x
plus
x2
times, the derivative of tan x, sec2 x.
Arrange the expression.
So
2x tan x + x2 sec2 x
is the derivative of x2 tan x.