We are going to differentiate sec x in various methods such as using the first principles definition of the derivative , quotient rule, and chain rule in the upcoming sections.
By first principle, the derivative of a function f x is,. Here are some topics that you may be interested in while studying about the differentiation of sec x. By one of the trigonometric identities ,. For more detailed proof, click here.
No, the derivative of sec x is NOT same as the derivative of sec -1 x. We know that the derivative of sec w is sec w tan w. We can prove that the derivative of sec x is sec x tan x using different methods. For detailed information, you can click on one of the following:. Learn Practice Download.
Derivative of Sec x Before going to find the derivative of sec x, let us recall a few things. We can find it using various ways such as: by using the first principle by using the quotient rule by using the chain rule Let us do the differentiation of sec x in each of these methods and we will solve a few problems using the derivative of sec x. What is Derivative of Sec x?
Derivative of Sec x by First Principle 3. Derivative of Sec x by Quotient Rule 4. The chain rule is useful for finding the derivative of a function which could have been differentiated had it been in x, but it is in the form of another expression which could also be differentiated if it stood on its own.
Although the expression sec 2 x contains no parenthesis, we can still view it as a composite function a function of a function. Now the function is in the form of x 2 , except it does not have x as the base, instead it has another function of x sec x as the base. The Chain Rule: For two differentiable functions f x and g x. Just be aware that not all of the forms below are mathematically correct.
It is interesting to note that the derivative of sec 2 x is equal to the derivative of tan 2 x.
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