Solved Examples on Derivative of Tan x
Some examples related to Derivative of Tan x are,
Example 1: Find the derivative of tan2x
Solution:
Let f(x) = tan2x = (tan x)2
By using power rule and chain rule,
f'(x) = 2 tan x.d/dx(tan x)
We know that the derivative of tan x is sec2x
f'(x) = 2 tan x · sec2x
Hence, derivative of the given function is 2 tan x·sec2x
Example 2: Differentiate tan x with respect to sec x.
Solution:
Let us assume v = tan x and u = sec x. Then dv/dx = sec2x and du/dx = sec x · tan x.
We have to find dv/du. We can write this as
dv/du = (dv/dx) / (du/dx)
= (sec2x) / (sec x·tan x)
= (sec x) / (tan x)
= (1/cos x) / (sin x/cos x)
= 1/sin x
= cosec x
Hence, derivative of tan x with respect to sec x is cos x.
Example 3: Find the derivative of tan x·sec2x
Solution:
Let f(x) = tan x·sec2x.
By product rule,
f'(x) = tan x·d/dx (sec2x) + sec2x · d/dx(tan x)
= tan x.(2 sec x) d/dx (sec x) + sec2x (sec2x) (by chain rule)
= 2 sec x tan x (sec x tan x) + sec4x
= 2 sec2x tan2x + sec4x
Hence, derivative of the given function is 2sec2x tan2x + sec4x
Derivative of Tan x
Derivative of Tan x is sec2x. Derivative of Tan x refers to the process of finding the change in the tangent function with respect to the independent variable. Derivative of tan x is also known as differentiation of tan x.
In this article, we will learn about the derivative of Tan x and its formula including the proof of the formula using the first principle of derivatives, quotient rule, and chain rule as well.
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