
What is the second derivative of ?
Answer
445.8k+ views
Hint: Here, the given question has a trigonometric function. We have to find the derivative or differentiated term of the function. We know the standard derivative of secant function and which is the first derivative. To find the second derivative we use product rule that is .
Complete step by step solution:
The differentiation of a function is defined as the derivative or rate of change of a function. The function is said to be differentiable if the limit exists.
Given .
Or
Now differentiate with respect to ‘x’, we have,
. This is the first derivative.
To find the second derivative we again differentiate the first derivative.
Using the product rule of differentiation, we have,
.
We know and ,
. This is the required result.
Thus the second derivative of is .
Additional information:
Linear combination rule: The linearity law is very important to emphasize its nature with alternate notation. Symbolically it is specified as
Quotient rule: The derivative of one function divided by other is found by quotient rule such as .
Product rule: When a derivative of a product of two function is to be found, then we use product rule that is .
Chain rule: To find the derivative of composition function or function of a function, we use chain rule. That is .
Note:
We know the differentiation of is . The first obtained result is the first derivative. If we differentiate again we get a second derivative. If we differentiate the second derivative again we get a third derivative and so on. Careful in applying the product rule. We also know that differentiation of constant terms is zero.
Complete step by step solution:
The differentiation of a function is defined as the derivative or rate of change of a function. The function is said to be differentiable if the limit exists.
Given
Or
Now differentiate with respect to ‘x’, we have,
To find the second derivative we again differentiate the first derivative.
Using the product rule of differentiation, we have,
We know
Thus the second derivative of
Additional information:
Note:
We know the differentiation of
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

How do I get the molar mass of urea class 11 chemistry CBSE

How do I convert ms to kmh Give an example class 11 physics CBSE

Where can free central placentation be seen class 11 biology CBSE

What is the molecular weight of NaOH class 11 chemistry CBSE

What is 1s 2s 2p 3s 3p class 11 chemistry CBSE
