What is the Derivative of sec x

Q. What Is The Derivative Of Sec X

Answer:- Before going ahead and finding the derivative of sec x, you should try to recall a few things related to trigonometry. 

• The relationship of tan x with sin x and cos x

tan x = sin x / cos x

• Cos x and sec x are inversely proportional to each other

Once you are aware of these two facts, you can go ahead with the differentiation of sec x. You can do this in various ways. For example, with the chain rule, by using the rule of first principle rule, or by using the quotient rule. Let us now solve the query, what is the differentiation of sec x.

Solution

The derivative of sec x with respect to the angle x is sec x. tan x. This is read as the product of sex x and tan x. We arrived at this result as follows:

We have f(x) = 1/cos x 

=  (- 1 )(-sin x)]/ cos2x

= (sin x) / cos2x

= (1/cos x ) (sin x)/(cos x)

= sec x · tan x

Hence the following solution satisfies the question of what derivative of sec x is.