Derive sec 2x

The derivative of sec square x at a point gives us the slope of graph of the function sec square x at that point.

The derivative of sec square x is equal to twice the product of sec square x and tanx. Differentiation of a function gives the slope function of the curve of the function which can give the slope of the function at a particular point. Let us learn to evaluate the derivative of sec square x using different methods of derivatives and its formula. We will also solve different examples related to the concept for a better understanding of the concept of derivatives. Sec x is one of the important and main trigonometric functions in trigonometry.

Derive sec 2x

Note that in this post we will be looking at differentiating sec 2x which is not the same as differentiating sec 2 x. 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. To perform the differentiation sec 2x , the chain rule says we must differentiate the expression as if it were just in terms of x as long as we then multiply that result by the derivative of what the expression is actually in terms of in this case the derivative of 2x. The Chain Rule: For two differentiable functions f x and g x. Now we can just plug f x and g x into the chain rule. But before we do that, just a quick recap on the derivative of the sec function. The derivative of sec x with respect to x is sec x tan x The derivative of sec z with respect to z is sec z tan z. In a similar way, the derivative of sec 2x with respect to 2x is sec 2x tan 2x. We will use this fact as part of the chain rule to find the derivative of sec 2x with respect to x. Using the chain rule, the derivative of sec 2x is 2sec 2x tan 2x. Finally, just a note on syntax and notation: sec 2x is sometimes written in the forms below with the derivative as per the calculation above. Just be aware that not all of the forms below are mathematically correct. So to find the second derivative of sec 2x , we just need to differentiate 2sec 2x tan 2x. We can use the chain rule to find the derivative of 2sec 2x tan 2x and it gives us a result of 8sec 3 2x — 4sec 2x.

Published by DerivativeIt. Sec x is one of the important and main trigonometric functions in trigonometry.

The first method is by using the product rule for derivatives since sec 2 x can be written as sec x. The product rule for differentiation states that the derivative of f x. The Product Rule: For two differentiable functions f x and g x. 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 comes up with a way to calculate the derivative of composite functions with both the number of functions in the composition identifying the number of differentiation steps required. When you take the derivative of the derivative of a function, this is called the second derivative of that function. Though the first derivative indicates whether the function is decreasing or increasing, the second derivative indicates whether the first derivative is decreasing or increasing. To calculate the second derivative of a function, you just need to differentiate the first derivative. Since the second derivative will be the derivative of a function having the product of two terms, therefore, the product rule will be used to work out the second derivative in this case. So the substitution of these values in the above formula will give us:. The chain rule is the method used to calculate the derivative of a composite function. The chain rule only applies to composite functions. The derivative of the composition of these two functions can be expressed using the chain rule. The secant of an angle in a right-angled triangle is the measure of the hypotenuse divided by the measurement of the adjacent side.

Derive sec 2x

The derivative of sec square x is equal to twice the product of sec square x and tanx. Differentiation of a function gives the slope function of the curve of the function which can give the slope of the function at a particular point. Let us learn to evaluate the derivative of sec square x using different methods of derivatives and its formula.

The position time graph for a particle of mass 1kg

Sec square x is an example of a composite function. The derivative of sec square x is twice the product of sec square x and tangent x. It is interesting to note that the derivative of sec 2 x is equal to the derivative of tan 2 x. Applications of Derivatives. Last updated on May 23, The image below shows the formula for the derivative of sec square x:. Differentiating this gives us the second derivative of sec square x. What is the Derivative of Sec Square x? Sri Lanka. The Chain Rule: For two differentiable functions f x and g x. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Product rule in differentiation is used when we need to find the derivative of the product of two functions.

Learn what is the derivative of sec square x with formula. Also understand how to prove the derivative of sec 2x by three techniques.

What is sec square x? Learn Practice Download. We can write sec 2 x as sec x 2. Online Tutors. Finally, just a note on syntax and notation: sec 2x is sometimes written in the forms below with the derivative as per the calculation above. Our Mission. What does sec 2 theta equal? Derivative of Sec Square x Questions. Derivative of Sec Square x using Chain Rule We use the chain rule for finding the derivative of composite functions. About Us. The Chain Rule: For two differentiable functions f x and g x. Learn about the Derivative of Root x and the Derivative of Sin 2x. View Test Series. 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.